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With the development of the IoT, Wireless Rechargeable Sensor Networks (WRSNs) derive more and more application scenarios with diverse performance requirements. In scenarios where the energy consumption rate of sensor nodes changes dynamically, most existing charging scheduling methods are not applicable. The incorrect estimation of node energy requirement may lead to the death of critical nodes, resulting in missing events. To address this issue, we consider both the spatial imbalance and temporal dynamics of the energy consumption of the nodes, and minimize the Event Missing Rate (EMR) as the goal. Firstly, an Energy Consumption Balanced Tree (ECBT) construction method is proposed to prolong the lifetime of each node. Then, we transform the goal into Maximizing the value of the Evaluation function of each node's Energy Consumption Rate prediction (MEECR). Afterwards, the setting of the evaluation function is explored and the MEECR is further transformed into a variant of the knapsack problem, namely "the alternating backpack problem", and solved by dynamic programming. After predicting the energy consumption rate of the nodes, a charging scheduling scheme that meets the Dual Constraints of Nodes' energy requirements and MC's capability (DCNM) is developed. Simulations demonstrate the advantages of the proposed method. Compared to the baselines, the EMR was reduced by an average of 35.2% and 26.9%. [ABSTRACT FROM AUTHOR]

Research and development of power factor corrector (PFC) for AC/DC converters of single-phase AC power supply network are discussed within this article. Two-channel bridgeless PFC is proposed in this paper. The proposed converter allows us to lower current DC component generation in the power network and to reduce static and dynamic losses of semiconductor devices. The suggested solution characteristic features are the absence of a diode bridge while using two identical converters operating in different power network voltage half periods. Due to cumulative chokes in each converter, the function setting the consumption current sinusoidal form is realized with the ability of wide-range output voltage regulation. A number of Simulink-models have been developed in order to study operating modes and to test control algorithms of the proposed bridgeless PFC. The input current harmonic content, efficiency coefficient, passive elements' electrical parameters, and output voltage pulsation coefficient of the proposed bridgeless PFC were researched by Simulink-models. The results obtained show the efficiency of the proposed solutions regarding PFC. The THD value does not exceed 1.3% in steady state mode and is not over 4% during the voltage stabilization process; the minimal value of the output voltage pulsation coefficient is 3.1%. The suggested solutions can be applied in accumulator batteries' charging sets and DC motors' reduced-current start. [ABSTRACT FROM AUTHOR]

Weakly supervised semantic segmentation (WSSS) aims to segment objects without a heavy burden of dense annotations. Pseudo-masks serve as supervisory information for training segmentation models, which is crucial to the performance of segmentation models. However, the generated pseudo-masks contain significant noisy labels, which leads to poor performance of the segmentation models trained on these pseudo-masks. Few studies address this issue, as these noisy labels remain inevitable even after the pseudo-masks are improved. In this paper, we propose an uncertainty-weight transform module to mitigate the impact of noisy labels on model performance. It is noteworthy that our approach is not aimed at eliminating noisy labels but rather enhancing the robustness of the model to noisy labels. The proposed method adopts a frequency-based approach to estimate pixel uncertainty. Moreover, the uncertainty of pixels is transformed into loss weights through a set of well-designed functions. After dynamically assigning weights, the model allocates attention to each pixel in a significantly differentiated manner. Meanwhile, the impact of noisy labels on model performance is weakened. Experiments validate the effectiveness of the proposed method, achieving state-of-the-art results of 69.3% on PASCAL VOC 2012 and 39.3% on MS COCO 2014, respectively. [ABSTRACT FROM AUTHOR]

This paper presents new classes of strong fuzzy negations, fuzzy implications and Copulas. It begins by presenting two theorems with function classes involving the construction of strong fuzzy negations. These classes are based on a well-known equilibrium point theorem. After that, a construction of fuzzy implication is presented, which is not based on any negation. Finally, moving on to the area concerning copulas, we present proof about the third property of copulas. To conclude, we will present two original constructions of copulas. All the above constructions are motivated by a specific formula. For some specific conditions of the variables x, y and other conditions for the function f(x), the formula presented produces strict and strong fuzzy negations, fuzzy implications and copulas. [ABSTRACT FROM AUTHOR]

This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a three-corner discontinuity. The provided data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve. [ABSTRACT FROM AUTHOR]

This paper proposed a two-dimensional steady-state field prediction approach that combines B-spline functions and a fully connected neural network. In this approach, field data, which are determined by corresponding control vectors, are fitted by a selected B-spline function set, yielding the corresponding best-fitting weight vectors, and then a fully connected neural network is trained using those weight vectors and control vectors. The trained neural network first predicts a weight vector using a given control vector, and then the corresponding field can be restored via the selected B-spline set. This method was applied to learn and predict two-dimensional steady advection–diffusion physical fields with absorption and source terms, and its accuracy and performance were tested and verified by a series of numerical experiments with different B-spline sets, boundary conditions, field gradients, and field states. The proposed method was finally compared with a generative adversarial network (GAN) and a physics-informed neural network (PINN). The results indicated that the B-spline neural network could predict the tested physical fields well; the overall error can be reduced by expanding the selected B-spline set. Compared with GAN and PINN, the proposed method also presented the advantages of a high prediction accuracy, less demand for training data, and high training efficiency. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced crayfish optimization algorithm (ECOA). The ECOA includes four improvement strategies. Firstly, the Halton sequence was used to improve the population initialization of the crayfish optimization algorithm. Furthermore, the quasi opposition-based learning strategy is introduced to generate the opposite solution of the population, increasing the algorithm's searching ability. Thirdly, the elite factor guides the predation stage to avoid blindness in this stage. Finally, the fish aggregation device effect is introduced to increase the ability of the algorithm to jump out of the local optimal. This paper performed tests on the widely used IEEE CEC2019 test function set to verify the validity of the proposed ECOA method. The experimental results show that the proposed ECOA has a faster convergence speed, greater performance stability, and a stronger ability to jump out of local optimal compared with other popular algorithms. Finally, the ECOA was applied to two real-world engineering optimization problems, verifying its ability to solve practical optimization problems and its superiority compared to other algorithms. [ABSTRACT FROM AUTHOR]

A timelike (TL) constant axis ruled surface in E 1 3 (Minkowski 3-space), as determined by its ruling, forms a constant dual angle with its Disteli-axis (striction axis or curvature axis). In this article, we employ the symmetry through point geometry of Lorentzian dual curves and the line geometry of TL ruled surfaces. This produces the capability to expound a set of curvature functions that specify the local configurations of TL ruled surfaces. Then, we gain some new constant axis ruled surfaces in Lorentzian line space and their geometrical illustrations. Further, we also earn several organizations among a TL constant axis ruled surface and its striction curve. [ABSTRACT FROM AUTHOR]

Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q -calculus. The class is proved to be not empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on | α 2 | and | α 3 | coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. [ABSTRACT FROM AUTHOR]

Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q -calculus. The class is proved to not be empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on | α 2 | and | α 3 | coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. [ABSTRACT FROM AUTHOR]

Graphs are a powerful tool for solving various mathematical problems. One such task is the representation of discrete structures. Combinatorial generation methods make it possible to obtain algorithms that can create discrete structures with specified properties. This article is devoted to issues related to the construction of such combinatorial generation algorithms for a wide class of directed lattice paths. The main method used is based on the representation of a given combinatorial set in the form of an AND/OR tree structure. To apply this method, it is necessary to have an expression for the cardinality function of a combinatorial set that satisfies certain requirements. As the main result, we have found recurrence relations for enumerating simple directed lattice paths that satisfy the requirements of the applied method and have constructed the corresponding AND/OR tree structure. Applying the constructed AND/OR tree structure, we have developed new algorithms for ranking and unranking simple directed lattice paths. Additionally, the obtained results were generalized to the case of directed lattice paths. [ABSTRACT FROM AUTHOR]

There are deep historical connections between symmetry, harmonic functions, and stratified sets. In this article, we prove an analog of the removable singularity theorem for bounded harmonic functions on stratified sets. The harmonic functions are understood in the sense of the soft Laplacian. The result can become one of the main technical components for extending the well-known Poincaré–Perron's method of proving the solvability of the Dirichlet problem for the soft Laplacian. [ABSTRACT FROM AUTHOR]

An enhanced dung beetle optimization algorithm (EDBO) is proposed for nonlinear optimization problems with multiple constraints in manufacturing. Firstly, the dung beetle rolling phase is improved by removing the worst value interference and coupling the current solution with the optimal solution to each other, while retaining the advantages of the original formulation. Subsequently, to address the problem that the dung beetle dancing phase focuses only on the information of the current solution, which leads to the overly stochastic and inefficient exploration of the problem space, the globally optimal solution is introduced to steer the dung beetle, and a stochastic factor is added to the optimal solution. Finally, the dung beetle foraging phase introduces the Jacobi curve to further enhance the algorithm's ability to jump out of the local optimum and avoid the phenomenon of premature convergence. The performance of EDBO in optimization is tested using the CEC2017 function set, and the significance of the algorithm is verified by the Wilcoxon rank-sum test and the Friedman test. The experimental results show that EDBO has strong optimization-seeking accuracy and optimization-seeking stability. By solving four engineering optimization problems of varying degrees, EDBO has proven to have good adaptability and robustness. [ABSTRACT FROM AUTHOR]

In this paper, a short review of the calculus of exact finite-differences of integer order is proposed. The finite-difference operators are called the exact finite-differences of integer orders, if these operators satisfy the same characteristic algebraic relations as standard differential operators of the same order on some function space. In this paper, we prove theorem that this property of the exact finite-differences is satisfies for the space of simple entire functions on the real axis (i.e., functions that can be expanded into power series on the real axis). In addition, new results that describe the exact finite-differences beyond the set of entire functions are proposed. A generalized expression of exact finite-differences for non-entire functions is suggested. As an example, the exact finite-differences of the square root function is considered. The use of exact finite-differences for numerical and computer simulations is not discussed in this paper. Exact finite-differences are considered as an algebraic analog of standard derivatives of integer order. [ABSTRACT FROM AUTHOR]

The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problems. However, in the rapid evolution of the adjoint function, some problems greatly limit the application of the adjoint function in the research of water resources. Therefore, based on bibliometric analysis, development, practical application issues, and prospects of the hot directions are analyzed. It is found that the development of the connection number of water resource set pair analysis can be divided into three stages: (1) relatively sluggish development before 2005, (2) a period of rapid advancement in adjoint function research spanning from 2005 to 2017, and (3) a subsequent surge post-2018. The introduction of the adjoint function of connection number promotes the continuous development of set pair analysis of water resources. Set pair potential and partial connection number are the crucial research directions of the adjoint function. Subtractive set pair potential has rapidly developed into a relatively independent and important trajectory. The research on connection entropy is comparatively less, which needs to be further strengthened, while that on adjacent connection number is even less. The adjoint function of set pair potential can be divided into three major categories: division set pair potential, exponential set pair potential, and subtraction set pair potential. The subtraction set pair potential, which retains the original dimension and quantity variation range of the connection number, is widely used in water resources and other fields. Coupled with the partial connection number, a series of new connection number adjoint functions have been developed. The partial connection number can be mainly divided into two categories: total partial connection number, and semi-partial connection number. Among these, the calculation expression and connotation of total partial connection numbers have not yet reached a consensus, accompanied by the slow development of high-order partial connection numbers. Semi-partial connection number can describe the mutual migration movement between different components of the connection number, which develops rapidly. With the limitations and current situation described above, promoting the exploration and application of the adjoint function of connection number in the field of water resources and other fields of complex systems has become the focus of future research. [ABSTRACT FROM AUTHOR]

A novel multi-objective robust optimization model of an integrated energy system with hydrogen storage (HIES) considering source–load uncertainty is proposed to promote the low-carbon economy operation of the integrated energy system of a park. Firstly, the lowest total system cost and carbon emissions are selected as the multi-objective optimization functions. The Pareto front solution set of the objective function is applied by compromise planning, and the optimal solution among them is obtained by the maximum–minimum fuzzy method. Furthermore, the robust optimization (RO) approach is introduced to cope with the source–load uncertainty effectively. Finally, it is demonstrated that the illustrated HIES can significantly reduce the total system cost, carbon emissions, and abandoned wind and solar power. Meanwhile, the effectiveness of the proposed model and solution method is verified by analyzing the influence of multi-objective solutions and a robust coefficient on the Chongli Demonstration Project in Hebei Province. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a membership function used to form the fuzzy Mandelbric set and investigate the structural effects of additive and multiplicative dynamic noises on it. The newly defined membership function of this fuzzy set and its perturbations is a generalization of the indicator function for the classical Mandelbric set. We present an algorithm for detecting each complex number's fuzzy membership degree. Through the use of the membership degrees of each complex number and experimental mathematics based on the visualizations of a variety of versions by utilizing computer-aided design, we gain a deep foresight for the structure characteristics of the additive and multiplicative perturbed fuzzy Mandelbric sets. Our novel approach allows us to identify the symmetry states of the Mandelbric set and its perturbations by the membership degrees of complex numbers, unlike the existing methods described in the literature. [ABSTRACT FROM AUTHOR]

The pathfinder algorithm (PFA) starts with a random search for the initial population, which is then partitioned into only a pathfinder phase and a follower phase. This approach often results in issues like poor solution accuracy, slow convergence, and susceptibility to local optima in the PFA. To address these challenges, a multi-strategy fusion approach is proposed in the symmetry-enhanced, improved pathfinder algorithm-based multi-strategy fusion for engineering optimization problems (IPFA) for function optimization problems. First, the elite opposition-based learning mechanism is incorporated to improve the population diversity and population quality, to enhance the solution accuracy of the algorithm; second, to enhance the convergence speed of the algorithm, the escape energy factor is embedded into the prey-hunting phase of the GWO and replaces the follower phase in the PFA, which increases the diversity of the algorithm and improves the search efficiency of the algorithm; lastly, to solve the problem of easily falling into the local optimum, the optimal individual position is perturbed using the dimension-by-dimension mutation method of t-distribution, which helps the individual to jump out of the local optimum rapidly and advance toward other regions. The IPFA is used for testing on 16 classical benchmark test functions and 29 complex CEC2017 function sets. The final optimization results of PFA and IPFA in pressure vessels are 5984.8222 and 5948.3597, respectively. The final optimization results in tension springs are 0.012719 and 0.012699, respectively, which are comparable with the original algorithm and other algorithms. A comparison between the original algorithm and other algorithms shows that the IPFA algorithm is significantly enhanced in terms of solution accuracy, and the lower engineering cost further verifies the robustness of the IPFA algorithm. [ABSTRACT FROM AUTHOR]

Many different aspects of software system development and verification rely on precise function identification in binary code. Recognition of the source Assembly functions in embedded systems is one of the fundamental challenges in binary program analysis. While numerous approaches assume that the functions are given a priori, correct identification of the functions in binaries remains a great issue. This contribution addresses the problem of uncertainty in binary code in identification of functions, which were optimized during compilation. This paper investigates the difference between debug and optimized functions via modeling of these functions. To do so, we introduce an extensible model-centred hands-on approach for examining similarities between binary functions. The main idea is to model each function using a set of predetermined, experimentally discovered features, and then find a suitable weight vector that could give impact factor to each such a feature. After finding the weight vector, the introduced models of such desired functions can be identified in binary software packages. It means that we reduce the similarity identification problem of the models to a classical version of optimization problems with one optimization criterion. Using our implementation, we found that the proposed approach works smoothly for functions, which contain at least ten Assembly instructions. Our tool guarantees success at a very high level. [ABSTRACT FROM AUTHOR]

This paper delves into an interference analysis, focusing on the forthcoming Starlink Generation 2 satellites, stated to operate within the 1990–1995 MHz frequency band. The aim is to assess the potential interference from this Starlink system to the satellite receivers of mobile satellite systems (MSSs), which are set to function within the 1980–2010 MHz range, and satellite receivers of the NTN systems, which are planned to operate in the n256 bands, defined by the 3GPP specifications. Through simulation-based evaluations, both single-entry and aggregate interference levels from Starlink to MSSs and NTN systems are comprehensively explored. To estimate the interference impact, several protection criteria were used. The study is in line with the Recommendations of International Telecommunication Union (ITU-R) and common approaches that are used when performing compatibility studies between satellite systems. The findings of this study demonstrate the feasibility of utilizing the n25 band for NTN direct-to-device services. [ABSTRACT FROM AUTHOR]

Plantarflexor central drive is a promising biomarker of neuromotor impairment; however, routine clinical assessment is hindered by the unavailability of force measurement systems with integrated neurostimulation capabilities. In this study, we evaluate the accuracy of a portable, neurostimulation-integrated, plantarflexor force measurement system we developed to facilitate the assessment of plantarflexor neuromotor function in clinical settings. Two experiments were conducted with the Central Drive System (CEDRS). To evaluate accuracy, experiment #1 included 16 neurotypical adults and used intra-class correlation (ICC2,1) to test agreement of plantarflexor strength capacity measured with CEDRS versus a stationary dynamometer. To evaluate validity, experiment #2 added 26 individuals with post-stroke hemiparesis and used one-way ANOVAs to test for between-limb differences in CEDRS' measurements of plantarflexor neuromotor function, comparing neurotypical, non-paretic, and paretic limb measurements. The association between paretic plantarflexor neuromotor function and walking function outcomes derived from the six-minute walk test (6MWT) were also evaluated. CEDRS' measurements of plantarflexor neuromotor function showed high agreement with measurements made by the stationary dynamometer (ICC = 0.83, p < 0.001). CEDRS' measurements also showed the expected between-limb differences (p's < 0.001) in maximum voluntary strength (Neurotypical: 76.21 ± 13.84 ft-lbs., Non-paretic: 56.93 ± 17.75 ft-lbs., and Paretic: 31.51 ± 14.08 ft-lbs.), strength capacity (Neurotypical: 76.47 ± 13.59 ft-lbs., Non-paretic: 64.08 ± 14.50 ft-lbs., and Paretic: 44.55 ± 14.23 ft-lbs.), and central drive (Neurotypical: 88.73 ± 1.71%, Non-paretic: 73.66% ± 17.74%, and Paretic: 52.04% ± 20.22%). CEDRS-measured plantarflexor central drive was moderately correlated with 6MWT total distance (r = 0.69, p < 0.001) and distance-induced changes in speed (r = 0.61, p = 0.002). CEDRS is a clinician-operated, portable, neurostimulation-integrated force measurement platform that produces accurate measurements of plantarflexor neuromotor function that are associated with post-stroke walking ability. [ABSTRACT FROM AUTHOR]

Optical rotation (OR), the most frequently used chiroptical method, is used for the characterization of newly synthesized or isolated compounds. Computational predictions of OR are, however, mainly used for the determination of the absolute configurations of chiral compounds, but they may also be used for the verification of conformational analysis results if the experimental values are known. Our computational study deals with the conformational analysis of flexible salicylamide-based peptidomimetics, starting with a conformation search, then a low-level ab initio preoptimization of the hundreds of conformations found, and, finally, a higher-level DFT optimization. For the resulting minima structures, Boltzmann populations were calculated, followed by OR calculations for all the populated conformers using the DFT method with various basis sets with diffuse functions. Weighted averages of the ORs were compared with experimental values, and the agreement, which ranged from excellent to moderate for various compounds, served as a verification of the conformational analysis results. [ABSTRACT FROM AUTHOR]

We present a non-traditional finite element method for the electromagnetic scattering of the partly covered groove filled with multiple media. The non-local boundary condition is introduced to make the unbounded scattering into a bounded domain problem. Non-body-fitted mesh is applied to save the cost of discretizing groove domain greatly. In addition, the level set functions are utilized to describe complex media interfaces and boundaries. Numerical tests demonstrate the effectiveness and second-order convergence rate of the proposed method. [ABSTRACT FROM AUTHOR]

In this research paper, we utilize the q-derivative concept to formulate specific differential and integral operators denoted as R q n , m , λ , F q n , m , λ and G q n , m , λ . These operators are introduced with the aim of generalizing the class of Ruscheweyh operators within the set of univalent functions. We extract certain properties and characteristics of the set of differential subordinations employing specific techniques. By utilizing the newly defined operators, this paper goes on to establish subclasses of analytic functions defined on an open unit disc. Additionally, we delve into the convexity properties of the two recently introduced q-integral operators, F q n , m , λ and G q n , m , λ . Special cases of the primary findings are also discussed. [ABSTRACT FROM AUTHOR]

Using metaheuristics such as the Evolutionary Algorithm (EA) within control structures is a realistic approach for certain optimal control problems. They often predict the optimal control values over a prediction horizon using a process model (PM). The computational effort sometimes causes the execution time to exceed the sampling period. Our work addresses a new issue: whether a machine learning (ML) algorithm could "learn" the optimal behaviour of the couple (EA and PM). A positive answer is given by proposing datasets apprehending this couple's optimal behaviour and appropriate ML models. Following a design procedure, a number of closed-loop simulations will provide the sequences of optimal control and state values, which are collected and aggregated in a data structure. For each sampling period, datasets are extracted from the aggregated data. The ML algorithm experiencing these datasets will produce a set of regression functions. Replacing the EA predictor with the ML model, new simulations are carried out, proving that the state evolution is almost identical. The execution time decreases drastically because the PM's numerical integrations are totally avoided. The performance index equals the best-known value. In different case studies, the ML models succeeded in capturing the optimal behaviour of the couple (EA and PM) and yielded efficient controllers. [ABSTRACT FROM AUTHOR]

In the grid-connected operation dynamics of brushless doubly fed generators (BDFGs), a dip in the grid voltage is equivalent to suddenly adding a reverse voltage source at the parallel node. By deriving the expressions of the transient current of power winding (PW), control winding (CW), and rotor winding (RW) of a BDFG in the complex frequency domain under a natural state, it was concluded that the overshoot and oscillation time are affected by the CW voltage, the drop degree and phase of the grid voltage, and the rotor speed. Therefore, an optimal control strategy is proposed. A state model with the CW current as the state variable was constructed using the Pontryagin minimum principle. The finite-time integral value of the square of the electromagnetic torque was set as the objective function to achieve the minimum value that could suppress the overshoot and oscillation of the electromagnetic torque, and the optimal CW voltage command value was directly solved to accelerate the convergence of the BDFG's physical quantities, thereby reducing the amplitude. Finally, the feasibility of the optimal control algorithm was verified using tests on an experimental platform. [ABSTRACT FROM AUTHOR]

This paper addresses the theoretical issues in k-valued logic, which are crucial for developing solutions in various fields of science and technology. One of the fundamental issues is a complete description of the closed classes of functions of three-valued logic. The explicit description of closed classes in multivalued logic is an open problem. In this study, we consider a special case of the finite generation of all closed classes of three-valued logic through the operation of superposition. Previously, we considered the issue of the finite generation of classes containing a subset of single-variable functions. We have also provided a description of superlattices (lattices of lattices) containing a precomplete class of unary functions. The finite generation of these superlattices is proved. On the basis of these results, in this paper, we have proven that any class containing any of the precomplete classes from the set of single-valued functions is also finitely generated. The main result of this paper consists of three theorems on the finite generation of classes containing precomplete classes of single-valued functions and classes including all monotone unary functions. Thus, the obtained theoretical result provides easily verifiable criteria for the finiteness of classes of multivalued logic functions. It allows you to use simple procedures instead of cumbersome explicit constructs. The finite generation of overlattices allows the development of digital computing circuits that are crucial for practical applications. The proofs are based on an explicit description of these classes by an induction in the number of variables and essentially use the properties of functionally closed (Burle) classes of functions. [ABSTRACT FROM AUTHOR]

In this paper, we prove some inequalities for Riemann–Lebesgue integrable functions when the considered integration is obtained via a non-additive measure, including the reverse Hölder inequality and the reverse Minkowski inequality. Then, we generalize these inequalities to the framework of a multivalued case, in particular for Riemann–Lebesgue integrable interval-valued multifunctions, and obtain some inequalities, such as a Minkowski-type inequality, a Beckenbach-type inequality and some generalizations of Hölder inequalities. [ABSTRACT FROM AUTHOR]

A new information theoretic condition is presented for reconstructing a discrete random variable X based on the knowledge of a set of discrete functions of X. The reconstruction condition is derived from Shannon's 1953 lattice theory with two entropic metrics of Shannon and Rajski. Because such a theoretical material is relatively unknown and appears quite dispersed in different references, we first provide a synthetic description (with complete proofs) of its concepts, such as total, common, and complementary information. The definitions and properties of the two entropic metrics are also fully detailed and shown to be compatible with the lattice structure. A new geometric interpretation of such a lattice structure is then investigated, which leads to a necessary (and sometimes sufficient) condition for reconstructing the discrete random variable X given a set { X 1 , ... , X n } of elements in the lattice generated by X. Intuitively, the components X 1 , ... , X n of the original source of information X should not be globally "too far away" from X in the entropic distance in order that X is reconstructable. In other words, these components should not overall have too low of a dependence on X; otherwise, reconstruction is impossible. These geometric considerations constitute a starting point for a possible novel "perfect reconstruction theory", which needs to be further investigated and improved along these lines. Finally, this condition is illustrated in five specific examples of perfect reconstruction problems: the reconstruction of a symmetric random variable from the knowledge of its sign and absolute value, the reconstruction of a word from a set of linear combinations, the reconstruction of an integer from its prime signature (fundamental theorem of arithmetic) and from its remainders modulo a set of coprime integers (Chinese remainder theorem), and the reconstruction of the sorting permutation of a list from a minimal set of pairwise comparisons. [ABSTRACT FROM AUTHOR]