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This paper considers the minimax design of two-dimensional (2D) finite impulse response (FIR) half-band filters. First, the design problem is formulated in a matrix form, where the half-band constraints are expressed as a pair of matrix equations. By matrix transformations, the constrained minimax problem is transformed into an unconstrained one. Then, we propose an efficient iterative reweighted least squares (IRLS) algorithm to solve this problem. The weighted least squares (WLS) subproblems arising from the IRLS algorithm are solved using a generalized conjugate gradient (GCG) algorithm. Moreover, the GCG algorithm is guaranteed to converge in a finite number of iterations. In the proposed algorithm, the design coefficients of filters are solved in their matrix form, leading to a great saving in computations and memory space. Design examples and comparisons with existing methods are provided to demonstrate the effectiveness and efficiency of the proposed algorithm.

[EN] Let A, B is an element of C-nxn with ind(A) = k and ind(B) = s and let L-B = (BB)-B-2(sic). A new condition (C-s,C-*): R(A(k)) boolean AND N((B-s)*) = {0} and R(B-s) boolean AND N((A(k))*) = {0}, is defined. Some new characterizations related to core-EP inverses are obtained when B satisfies condition (C-s,C-*). Explicit expressions of B(sic) and BB(sic) are also given. In addition, equivalent conditions, which guarantee that B satisfies condition (C-s,C-*), are investigated. We proved that B satisfies condition (C-s,C-*) if and only if L-B has a fixed matrix form. As an application, upper bounds for the errors parallel to B(sic) - A(sic)parallel to/parallel to A(sic)parallel to and parallel to BB(sic) - AA(sic)parallel to are studied. (c) 2021 Elsevier B.V. All rights reserved., The authors thank the Editor and Reviewers sincerely for their constructive comments and suggestions which have improved the quality of the paper. This research is supported by the National Natural Science Foundation of China (Nos. 11771076, 11871145), the Postgraduate Research and Practice Innovation Program of Jiangsu Province (No. KYCX18 -0053), the China Scholarship Council (File No. 201906090122). The third author is partially supported by Ministerio de Economia y Competitividad of Spain (grant Red de Excelencia MTM2017-90682-REDT) and partially supported by Universidad de Buenos Aires, Argentina. EXP-UBA: 13.019/2017, 20020170100350BA

A numerical method is proposed for the shaping of tools used in machining complex surfaces with a periodical profile, including screw surfaces. A heuristic approach to Mathcad programming is adopted. The mathematical formulation includes a module generating spatial transformations of the coordinate systems in matrix form. On that basis, a numerical model of a hob profile is constructed. This approach permits single-stage shaping, without determining the profile of the associated helical gear.

This paper presents the dynamic model of multibody systems driven by electric motors, the so-called electromechanical systems. The mechanical systems considered in this study include an open loop and/or a closed loop, a full-actuated and an under-actuated one. The dynamic model of this electromechanical systems is established in matrix form by applying the Lagrangian equation with and without multipliers and substructure method. With this approach it is easy to obtain the differential equation of motion of the electro-mechanical systems based on the corresponding differential equations of the purely available mechanical system. These obtained equations describe the electromechanical systems in engineering better in case the systems are purely described by mechanical equations. The differential equations of serial and parallel manipulators, slider-crank mechanism, and overhead crane driven by electric motors are established as illustrated examples. In addition, a simplified dynamic model obtained by neglecting of current variation is also validated by numerical simulations.

Proton irradiation induced Nb redistribution in Zr-xNb alloys (x = 0.4, 0.5, 1.0 wt%) has been investigated using scanning transmission electron microscopy/energy dispersive X-ray spectroscopy (STEM/EDS). Zr-xNb alloys are mainly composed of Zr matrix, native Zr–Nb–Fe phases, and β-Nb precipitates. After 2 MeV proton irradiation at 350 °C, a decrease of Nb content in native precipitates, as well as irradiation-induced precipitation of Nb-rich platelets (135 ± 69 nm long and 27 ± 12 nm wide) were found. Nb-rich platelets and Zr matrix form the Burgers orientation relationship, [ 1 1 ¯ 1 ]//[ 2 1 ¯ 1 ¯ 0 ] and (011)//(0002). The platelets were found to be mostly coherent with the matrix with a few dislocations near the ends of the precipitate. The coherent strain field has been measured in the matrix and platelets by the 4D-STEM technique. The growth of Nb-rich platelets is mainly driven by coherency and dislocation-induced strain fields. Irradiation may both enhance the diffusion and induce segregation of interstitial Nb to the ends of the irradiation induced platelets, further facilitating their growth.

Typical configuration of an unmanned towed underwater system (UTUS) was described and advantages of using this type of marine equipment for shallow depth works were outlined. A list of basic operating modes of the UTUS which are key modes for design calculations of the system was determined. Basic requirements to the design and construction of a competitive UTUS for shallow water areas have been formed. The main requirements include the need for high-performance underwater technologies and the use of state-of-the-art computer research and design software. The need to maximize use of materials, parts and units that are commercially available as components for the UTUS was also indicated. Expediency and possibility of applying the systems approach methodology at early stages of the UTUS design were shown. Equations of existence were formulated in a matrix form for the UTUS components which make it possible to check engineering solutions for compliance with the requirements of the Requirements Specification already at the stages of technical proposal and sketch design. Structural, power, information and operational characteristics of the UTUS components were used as the compliance criteria. Sequence of the design works was completed in a form of a generalized design algorithm that implements the systems approach using modern computer technologies and equations of the UTUS existence. The developed algorithm allows the designer to check requirements of the Requirements Specification already at the early stages of the UTUS design and forms a scientifically substantiated methodological basis for creation of competitive underwater equipment

Two-phase composites with n equal non-overlapping inclusions randomly embedded in the matrix are investigated. It is considered the case when the inclusions are bounded by some Lyapunov’s boundary curve. The problem is reduced to a vector-matrix problem of dimension n for one inclusion. The generalized alternating method of Schwarz applied to the vector-matrix problem is decomposed onto n scalar problems for one inclusion which are solved numerically by the method of integral equations for any smooth shape of the inclusions. A symbolic computation method is developed to solve the same problem by means of conformal mapping and functional equations. As a purpose, the effective conductivity of such models is exactly expressed through all geometrical and mechanical properties of its components.

In this paper, we propose a new matrix form to generate all 3 × 3 involutory and MDS matrices over F 2 m and prove that the number of all 3 × 3 involutory and MDS matrices over F 2 m is ( 2 m − 1 ) 2 ⋅ ( 2 m − 2 ) ⋅ ( 2 m − 4 ) , where m > 2 . Moreover, we give 3 × 3 involutory and MDS matrices over F 2 3 , F 2 4 and F 2 8 defined by the irreducible polynomials x 3 + x + 1 , x 4 + x + 1 and x 8 + x 7 + x 6 + x + 1 , respectively, by considering the minimum XOR count, which is a metric used in the estimation of hardware implementation cost. Finally, we provide the maximum number of 1s in 3 × 3 involutory MDS matrices.

In this work, we present a solution of the Boussinesq equation, which models shallow water waves. A powerful inverse scattering approach of Deift–Tomei–Trubowitz was published in 1982 for solving this equation in the Schwartz class. We rewrite the corresponding Lax pair in a matrix form and show that a recently developed theory of evolutionary nodes is applicable. As a result, we can locally solve this equation with analytic initial conditions on the line, providing a formula for the tau function, which defines where the solutions exist. More generally, arbitrary analytic solution is shown to arise from a vessel.

Purpose The paper aims to present a systematic conceptual analysis of the problem of organizational goal and to reduce the insights into it provided by the main conceptions taken in their development from one to another, to break out of the ruling paradigm and outline a new solution. Design/methodology/approach The study has been carried out from the historical and critical perspective. Findings The paper discovers the logic of the evolution the approaches to organizational goals have undergone and portrays it in a matrix form in the heart of which is the “zigzag effect”: each posterior stage returns to the essential elements rejected by those preceding it, and the last stage, being diametrically opposite to the first, is, at that, as well as the latter, akin to the intermediate stages. The opportunities afforded by the current paradigm have been exhausted and it seems to run to an impasse. Instead, the author suggests a new frame of orientation: organizational goals are closely interknit with personal, but not reducible to them and bear fundamentally transpersonal character, while the mechanism of involving the preferences of individuals and groups in goal-setting is based on the self-contained interests of the organization they pertain to. Research limitations/implications The findings, conclusions and generalizations obtained can serve for a necessary ground to researchers getting deeper into the essence of what bonds organizational life and activity. Practical implications The material empowers practitioners to comprehend the difficulties of framing cohesive goal and find efficient ways to overcome them. It is of value also to the teachers seeking to present a more exact and elaborate view of teleological foundations of management and organization theory. Originality/value Both the conceptual analysis of the evolution of the approaches to organizational goals and the author’s exposition of its logic and vision of their nature are provided for the first time.

We prove the Hausdorff measure version of the matrix form of Gallagher’s theorem in the inhomogeneous setting, thereby proving a conjecture posed by Hussain and Simmons [‘The Hausdorff measure version of Gallagher’s theorem—closing the gap and beyond’, J. Number Theory186 (2018), 211–225].

A complete mathematical model for measuring the parameters of the scattering matrix for a measurement object [Sx] in the form of a four-port network is developed, in which the mathematical model of the eight-port error is described by 16 parameters of the scattering matrix [E]. In addition, in comparison with the 12-parameter model of the eight-port error network, four parameters are included, which allow taking into account leaks, parasitic transmissions of microwave modules under study (microwave microassemblies). Due to the use of matrix analysis methods, the equations in matrix form are obtained that connect the matrices of the measurement object [Sи] and the actual values of the matrix parameters [Sx], with the aim of enabling the solution of these equations instead of the scattering matrix [E] to use a transmition matrix [T] in the form of cellular matrices [Taa], [Tab], [Tba], [Tbb].

In this paper, we discuss the design and analysis of polynomial time algorithms for two problems associated with a linearly infeasible system of Unit Two Variable Per Inequality (UTVPI) constraints, viz., (a) the read-once refutation (ROR) problem, and (b) the literal-once refutation (LOR) problem. Recall that a UTVPI constraint is a linear relationship of the form: $$a_{i}\cdot x_{i}+a_{j} \cdot x_{j} \le b_{ij}$$ , where $$a_{i},a_{j} \in \{0,1,-1\}$$ . A conjunction of such constraints is called a UTVPI constraint system (UCS) and can be represented in matrix form as: $$\mathbf{A \cdot x \le b}$$ . These constraints find applications in a host of domains including but not limited to operations research and program verification. For the linear system $$\mathbf{A\cdot x \le b}$$ , a refutation is a collection of m variables $$\mathbf{y}=[y_{1},y_{2},\ldots , y_{m}]^{T} \in \mathfrak {R}^{m}_{+}$$ , such that $$\mathbf{y\cdot A =0}$$ , $$\mathbf{y \cdot b } < 0$$ . Such a refutation is guaranteed to exist for any infeasible linear program, as per Farkas’ lemma. The refutation is said to be read-once, if each $$y_{i} \in \{0,1\}$$ . Read-once refutations are incomplete in that their existence is not guaranteed for infeasible linear programs, in general. Indeed they are not complete, even for UCSs. Hence, the question of whether an arbitrary UCS has an ROR is both interesting and non-trivial. In this paper, we reduce this problem to the problem of computing a minimum weight perfect matching (MWPM) in an undirected graph. This transformation results in an algorithm that runs in in time polynomial in the size of the input UCS. Additionally, we design a polynomial time algorithm (also via a reduction to the MWPM problem) for a variant of read-once resolution called literal-once resolution. The advantage of reducing our problems to the MWPM problem is that we can leverage recent advances in algorithm design for the MWPM problem towards solving the ROR and LOR problems in UCSs. Finally, we show that another variant of read-once refutation problem called the non-literal read-once refutation (NLROR) problem is NP-complete in UCSs.

Thermal behavior of integrated passive components has become an important issue when designing these components. This paper presents the thermal modeling of a multilayer integrated LC filter used in DC-DC step-down converter for temperature distribution calculation. The approach used for this analysis is based on thermal equivalent circuit. Temperature distribution is obtained from algebraic equation, which is in vector and matrix form. The results of analytical calculation are compared with simulation results from finite element method. These results showed a good correlation.

OBJECTIVES: Research have identified large individual variation in physiological response to diet, which has led to more focused investigations in precision nutrition. One approach towards personalized nutrition is to identify groups of differential responders, so called metabotypes (i.e., clusters of individuals with similar metabolic profiles and/or regulation). Metabotyping has previously been addressed using matrix decomposition tools like principal component analysis (PCA) on data organized in matrix form. However, metabotyping using data from more complex experimental designs, involving e.g., repeated measures over time or multiple treatments (tensor data), requires new methods. METHODS: We developed a workflow for detecting metabotypes from experimental tensor data. The workflow is based on tensor decomposition, specifically PARAFAC which is conceptually similar to PCA but extended to multidimensional data. Metabotypes, based on metabolomics data were identified from PARAFAC scores using k-means clustering and validated by their association to anthropometric and clinical baseline data. Additionally, we evaluated the robustness of the metabotypes using bootstrapping. Furthermore, we applied the workflow to identify metabotypes using data from a crossover acute post-prandial dietary intervention study on 17 overweight males (BMI 25–30 kg/m2, 41–67 y of age) undergoing three dietary interventions (pickled herring, baked herring and baked beef), measuring 80 metabolites (from GC-MS metabolomics) at 8 time points (0–7h). RESULTS: We identified two metabotypes characterized by differences in amino acid levels, predominantly in the beef diet, that were also associated with creatinine (p = 0.007). The metabotype with higher postprandial amino acid levels was also associated with higher fasting creatinine compared to the other metabotype. CONCLUSIONS: The results stress the potential of PARAFAC to discover metabotypes from complex study designs. The workflow is not restricted to our data structure and can be applied to any type of tensor data. However, PARAFAC is sensitive to data pre-processing and further studies where differential metabotypes are related to clinical endpoints are highly warranted. FUNDING SOURCES: This work has been supported by the Swedish Foundation for Strategic Research and Formas, which is gratefully acknowledged.

Computational prediction of drug–target interactions (DTIs) is of particular importance in the process of drug repositioning because of its efficiency in selecting potential candidates for DTIs. A variety of computational methods for predicting DTIs have been proposed over the past decade. Our interest is which methods or techniques are the most advantageous for increasing prediction accuracy. This article provides a comprehensive overview of network-based, machine learning, and integrated DTI prediction methods. The network-based methods handle a DTI network along with drug and target similarities in a matrix form and apply graph-theoretic algorithms to identify new DTIs. Machine learning methods use known DTIs and the features of drugs and target proteins as training data to build a predictive model. Integrated methods combine these two techniques. We assessed the prediction performance of the selected state-of-the-art methods using two different benchmark datasets. Our experimental results demonstrate that the integrated methods outperform the others in general. Some previous methods showed low accuracy on predicting interactions of unknown drugs which do not exist in the training dataset. Combining similarity matrices from multiple features by data fusion was not beneficial in increasing prediction accuracy. Finally, we analyzed future directions for further improvements in DTI predictions.

Dynamic models play an important role in parallel manipulators simulation and control. Mainly in the later case, the efficiency of the involved computations is of paramount importance, because manipulator real-time control is usually necessary (Zhao & Gao, 2009). The dynamic model of a parallel manipulator operating in free space can be represented in Cartesian coordinates by a system of nonlinear differential equations, which may be written in matrix form as       f x G x x x V x x I          , (1)

Definition of frame-invariant Soret coefficients for ternary mixtures The definition of the Soret coefficient of a binary mixture includes a concentration prefactor, x(1-x) when mol fraction x is used, or w(1-w) when mass fraction w is used. In this presentation the physical reasons behind this choice are reviewed, emphasizing that the use of these prefactors makes the Soret coefficient invariant upon change in the reference frame, either mass or molar. Then, it will be shown how this invariance property can be extended to ternary mixtures by using an appropriate concentration prefactor in matrix form. The presentation will be completed with some considerations of general non-isothermal diffusion fluxes, binary limits of the concentration triangle, selection of the dependent concentration in a ternary mixture, and, finally, extension to multi-component mixtures.References[1] J. M. Ortiz de Zarate. Definition of frame-invariant thermodiffusion and Soret coefficients for ternary mixtures. Eur. Phys. J. E 42(2019), 43

We explore a case example of hybridity between a large worker-owned cooperative and a union through three lenses: organizational forms, multiple institutional logics, and organizational identity. We delineate three types of organizational hybridity: (1) stretching an existing organizational form; (2) creating a new organizational form; and (3) and retaining multiple discrete organizational forms in a common venture. The cooperative–union hybrid shares members from the two contributing organizations, and so can be classified as a matrix sub-form of multi-organizational hybridity. This study describes how the coop-union hybrid manages the multiple logics and identities retained from both contributing organizations. It considers the hazards of combining these logics and identities, and offers some suggestions on how to avoid potential difficulties. Finally, given the complexity and inefficiencies of the matrix form, we explore whether matrix hybridity is a transitional or permanent form in this particular instance of a cooperative–union venture.

In this article, the solution of the task of determining optimal strategies of collaborative decision making by the remote pilot and air traffic controller as a problem of resolving the “conflict” between them by the methods of game theory is presented. Example of the model of conflict situation “remote pilot – air traffic controller” in flight emergency “Engine failure and fire on unmanned aerial vehicle during climbing after take-off’ is given.

A methodology is presented to decouple and isolate the separate solutions of a set of coupled partial differential equations describing the heat, mass, and surface energy transfer in nanomaterials and surface films. Calculation of the eigenvalues and eigenvectors give the solution in matrix form, whereby the stability and other characteristics of the solution are known. For illustration a binary set is chosen, however, the method is capable of extension to more than two coupled systems. Applications to radiation and radar-absorbing and attenuating surfaces for defence and consumer uses are envisaged.

In this paper, the task of performing finite-length minimum mean square error (MMSE) equalization is considered for single carrier communication systems. A detailed mathematical derivation of the finite-length MMSE equalizer is presented where the MMSE equalizer coefficients are described using linear convolution instead of the matrix form representation, which is commonly found in literature. The linear convolution is then transformed into circular convolution by performing frequency-domain sampling while avoiding time-domain aliasing. The computation of the circular convolution naturally lends itself to employing FFT and IFFT operations, which leads to a significant complexity reduction compared to the traditional approaches of computing the MMSE equalizer coefficients using matrix inversion.

In this article, we study linear barycentric rational method (LBM) to solve one-order Volterra integro-differential equations. With the help of linear barycentric rational interpolation, the matrix form of Volterra integro-differential equations is obtained. Then the convergence rate of LBM for solving one-order integro-differential equation is proved. Further more, Volterra integro-differential equation systems is also solved by the linear barycentric rational method. At last, several examples are presented to valid our theoretical analysis.

Mass transfer of protectant chemicals is a fundamental aspect of cryopreservation and freeze drying protocols. As such, mass transfer modeling is useful for design of preservation methods. Cell membrane transport modeling has been successfully used to guide design of preservation methods for isolated cells. For tissues, though, there are several mass transfer modeling challenges that arise from phenomena associated with cells being embedded in a tissue matrix. Both cells and the tissue matrix form a barrier to the free diffusion of water and protective chemicals. Notably, the extracellular space becomes important to model. The response of cells embedded in the tissue is dependent on the state of the extracellular space which varies both spatially and temporally. Transport in the extracellular space can also lead to changes in tissue size. In this chapter, we describe various mass transfer models that can be used to describe transport phenomena occurring during loading of tissues with protective molecules for cryopreservation applications. Assumptions and simplifications that limit the applicability of each of these models are discussed.

A spectral collocation method is developed to solve a nonlinear Caputo fractional differential system. The main idea is to solve the corresponding system of weakly singular nonlinear Volterra integral equations (VIEs). The convergence analysis in matrix form shows that the presented method has spectral convergence. Numerical experiments are carried out to confirm theoretical results.

The issues of the interaction of sea and land transport during the transportation of perishable goods are especially in demand at present in connection with the active development of intermodal transport. In addition, due to the rapidly changing specifics of the transport and logistics infrastructure in ports and terminals, the organization of transportation of perishable goods, which are especially vulnerable in terms of quality, requires new approaches and methods. The paper notes the high importance of preliminary preparation for the process of interaction between marine and land transport by operators of marine and land transport. On the part of the marine transport operator, it is advisable to focus on the pre-contractual work and clarification of the conditions for the formation of the freight rate; on the part of the land transportation operator, in the process of preliminary preparation, the state of the transport network for transporting refrigerated cargo near the port is of great importance. The paper proposes two new indicators for assessing the state of the transport network for the transportation of refrigerated goods. At the end of the paper, a model of the interaction of sea and land transport during the transportation of perishable goods with the expression of the multitude of cargo flows of perishable goods in the port through the matrix form is presented.

Data analytics allows an analyst to gain insight into underlying populations through the use of various computational approaches, including Monte Carlo methods. This paper discusses an approach to apply Monte Carlo methods to hedonic games. Hedonic games have gain popularity over the last two decades leading to several research articles that are concerned with the necessary, sufficient, or both conditions of the existence of a core partition. Researchers have used analytical methods for this work. We propose that using a numerical approach will give insights that might not be available through current analytical methods. In this paper, we describe an approach to representing hedonic games, with strict preferences, in a matrix form that can easily be generated; that is, a hedonic game with randomly generated preferences for each player. Using this generative approach, we were able to create and solve, i.e., find any core partitions, of millions of hedonic games. Our Monte Carlo experiment generated games with up to thirteen players. The results discuss the distribution form of the core size of the games of a given number of players. We also discuss computational considerations. Our numerical study of hedonic games gives insight into the underlying properties of hedonic games., Comment: 44 pages

In this paper, we extend use the spectral scheme by including a new application for solving the two-dimensional time-space fractional bioheat equation (T-SFBHE) with initial/Neumann boundary conditions. To achieve this goal, we suggest the numerical algorithm that depend on shifted Jacobi-Gauss-Lobatto polynomials (SJ-GL-Ps) together with Jacobi-Gauss-Lobatto points to calculate the approximate derivatives of any order (fractional/ordinary) in the matrix form. the proposed technique of the two examples is applied in order to evidence its utility and precision. The numerical results designate that the utilized approach is very effectual and gives high accuracy and good convergence by using a few grid points.

The objective in this research is to apply the recurrence neural network for car manufacturing with economy sentiment. The process applies two parallel mathematical methods from matrix approach and graph representation. First the randomly changes in production lines are studied regardless of economy sentiment. Secondly the change of production lines is considered in the case of changing economy sentiment. Thirdly the combination of the two processes in matrix form and graph form is constructed. It is seen that the graph, nodes and recursive process approach will lead to the recurrent neural network as timely sequence process. The development of the matrix conversion to graph representation is done and explained in figures in detail.

Quantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang-Mills theory. We illustrate the procedure for the toy electroweak model., 16 pages, 2 figures, changed equation numbering

This paper represents a simulation-based investigation of permissions in obfuscated android malware. Android malware detection has become a challenging and emerging area to research in information security because of the rapid growth of android based smartphone users. To detect malwares in android, permissions to access the functionality of android devices play an important role. Researchers now can easily detect the android malwares whose patterns have already been identified. However, recently attackers started to use obfuscation techniques to make the malwares unintelligible. For that reason, it’s necessary to identify the pattern used by attackers to obfuscate the malwares. In this paper, a large-scale investigation has been performed by developing python scripts to extract the pattern of permissions from an obfuscated malwares dataset named Android PRAGuard Dataset. Finally, the patterns in a matrix form has been found and stored in a Comma Separated Values (CSV) file which will lead to the fundamental basis of detecting the obfuscated malwares.

In this paper, we give quadratic approximation of generalized Tribonacci sequence $\{V_{n}\}_{n\geq0}$ defined by Eq. (\ref{eq:7}) and use this result to give the matrix form of the $n$-th power of a companion matrix of $\{V_{n}\}_{n\geq0}$. Then we re-prove the cubic identity or Cassini-type formula for $\{V_{n}\}_{n\geq0}$ and the Binet's formula of the generalized Tribonacci quaternions., Comment: 10 pages

In this note, we described two strategies for converting a Chebyshev polynomial to an ordinary polynomial with series of powers form. For this work we used of recursive sequences and matrix form fo...

espanolEn este articulo, se muestra una aplicacion y avance al metodo que permite encontrar de manera simple los coeficientes constantes que se requieren en la solucion de una ecuacion diferencial con la estructura de Cauchy-Euler, presentada y dada a conocer en [1]. Aqui veremos la forma de construccion de los polinomios caracteristicos, utilizando el metodo mencionado anteriormente como base; con una serie de ecuaciones, matrices y metodos novedosos para resolver este tipo de EDO y, sobre todo, muy practicas para la solucion de la ecuacion de orden superior. La idea es presentar una estructura o metodologia en forma matricial que permita resolver de manera practica la ecuacion diferencial de orden superior con la estructura de Cauchy-Euler. EnglishIn this article application and advance is given to the method that allows to find in a simple way the constant coefficients that are required in the solution of a differential equation with the structure of Cauchy-Euler, presented and made known in [1]. Here we will see the construction form of the characteristic polynomials, using the aforementioned method as a basis; with a series of equations, matrices and novel methods to solve this type of ODEs and, above all, very practical for the equation of a much higher order. The idea is to present a structure or methodology in matrix form that allows to solve in a practical way differential equation of higher order with Cauchy-Euler structure.

Equations of the theory of steady-state complex reactions are considered in matrix form. A set of stage stationarity equations is given, and an algorithm is described for deriving the canonic set of stationarity equations with appropriate corrections for the existence of fast stages in a mechanism. A formula for calculating the number of key compounds is presented. The applicability of the Gibbs rule to estimating the number of independent compounds in a complex reaction is analyzed. Some matrix equations relating the rates of dependent and key substances are derived. They are used as a basis to determine the general diffusion stoichiometry relationships between temperature, the concentrations of dependent reaction participants, and the concentrations of key reaction participants in a catalyst grain. An algorithm is described for calculating heat and mass transfer in a catalyst grain with respect to arbitrary complex heterogeneous catalytic reactions.

This paper has analyzed the Russian ICT Ecosystem based on the concept of innovation ecosystems. A qualitative model of the ICT Ecosystem (in the matrix form) has been proposed that is based on an analysis of the exchange of resources (commodity-material resources, current financial resources, capital, manpower resources) among participants in the ecosystem. The constructed quality model and primary analysis of the statistical data were used as the basis for obtaining a number of important conclusions regarding the structural features of the Russian ICT Ecosystem.

We study the strategic interaction between a new good producer and a remanufacturer who use advertising campaigns to compete for a dominant share of the market for a certain good. Each firm chooses one of three possible strategies for running its advertising campaign. The two rival firms care only about capturing a dominant share of the relevant market. Hence, if a firm expects to capture dominant market share with probability p є [0, 1], then its payoff in the game we study is also p. Our analysis leads to four results. First, we provide the normal form representation of the game between the new good producer and the remanufacturer. Second, we specify the game in matrix form. Third, we indicate what happens at each stage of the elimination of strictly dominated strategies. Finally, we show that the iterated elimination of strictly dominated strategies yields a clear and unique prediction about the outcome of the advertising game.

Precision machine tools are usually installed on foundations via supporting elements. In this configuration, errors because of inappropriate support lengths (level error) have to be adjusted during the installation to align the level of the machine tool. Consequently, a quantitative indication of level errors is a necessity for levelling works. Therefore, a model-based approach for level condition monitoring, which can identify level errors, is proposed. In the model, machine supports are modeled as linear springs. The relationship between the level error and preload distribution is modeled in matrix form. This report verifies the fundamentals of the proposed approach through experiments performed on a machining center.

Research is of little use if its results are not effectively communicated. Data visualised in graphs (and tables) are key components in any scientific report, but their design leaves much to be desired. This viewpoint focuses on graph design, following two general principles: clear vision and clear understanding. Clear vision is achieved by maximising the signal to noise ratio. In a graph, the signal is the data in the form of symbols, lines or other graphic elements, and the noise is the support structure necessary to interpret the data. Clear understanding is achieved when the story in the data is told effectively, through organisation of the data and use of text. These principles are illustrated by original and improved graphs from recent publications, completed by tutorial material online (appendices, web pages and film clips). The popular matrix form (multiple graphs in one frame) is discussed as a special case. Differences between publication (including the proofing stage) and presentation are outlined. Suggestions are made for better peer review and processing of graphs in the publication stage.

Inspired by an old result by Georg Frobenius, we show that the unbiased version of Hall’s marriage theorem is more transparent when reformulated in the language of matrices. At the same time, we ob...

A way of detecting local anisotropies of the muon flux using the matrix-form data of the URAGAN hodoscope (MEPhI) is proposed. Confidence intervals for estimating the matrix-data mathematical expectations in observations with reference and sliding data-sampling periods are selected, indicator functions are constructed, and a procedure for space–time filtering is developed. The results are presented from a search for local anisotropy in the muon flux recorded in the matrix-form data of the URAGAN hodoscope.

This paper presents a new formulation for analyzing a beam on elastic supports traveling on irregular profiles. The model is a first approximation of a passenger railway vehicle car body. The main difference with previous works is the use of a complex modulus to represent structural damping rather than relying on equivalent viscous terms. The formulation groups rigid body modes with flexible modes and proposes a matrix form that is easy to interpret and solve in the frequency domain. Comfort indexes are readily obtained from weighted response spectral densities. The model is used to assess the influence of structural damping and stiffness on comfort. It will be shown that the evolution of comfort with stiffness is non-monotonic and, therefore, comfort does not always improve as stiffness increases.

This research presents a methodology for creating mivar knowledge bases in tabular-matrix form for ground intelligent vehicle control systems. At its core, this methodology is kind of instruction for analysts facing the task of formalizing knowledge in a given subject area. The result of this formalization is a “knowledge map” created according to a special proposed template. In the future, this template allows forming a knowledge base for a given subject area in the formalism of bipartite oriented mivar networks. As an example, the subject area of ground-based intelligent vehicle control systems is used as a template. The proposed methodology of knowledge formalization makes it possible to simplify the process of creating models in Wi!Mi “Razumator-Consultant” 2.1 and also to level the probability of logical collisions when designing a knowledge model in the formalism of bipartite oriented mivar networks.

We study the Schlesinger system of partial differential equations in the case when the unknown matrices of arbitrary size ( p × p ) are triangular and the eigenvalues of each matrix form an arithmetic progression with a rational difference q , the same for all matrices. We show that such a system possesses a family of solutions expressed via periods of meromorphic differentials on the Riemann surfaces of superelliptic curves. We determine the values of the difference q , for which our solutions lead to explicit polynomial or rational solutions of the Schlesinger system. As an application of the ( 2 × 2 ) -case, we obtain explicit sequences of rational solutions and of one-parameter families of rational solutions of Painleve VI equations. Using similar methods, we provide algebraic solutions of particular Garnier systems.