Concept Of Matrix Research Articles

Total Energy of Cycle and Some Cycle Related Graphs

In this article we write algorithms and MATLAB programs to find the total energy of Cycle and some Cycle related graphs. The concept of total matrix and total energy of a graph G is introduced by K.Palani&M.Lalithakumari in [9]. Let G=(V, E) be a (p, q) simple graph. Let V (G) = {ν i /i = 1,2, … p} and E (G) = {e i /i = 1,2, … q}. The total matrix T = T(G) of G is a square matrix of order p + q whose (i, j)-entry is defined as: The Total Energy of a graph is the sum of absolute value of the eigen values of its Total matrix T(G). For any (p, q) graph G, the total number of eigen value is p+q.Let λ 1, λ 2, λ 3, … λ p+q be the eigen values of T. Then total energy of G is T E = .

The number of Dirac‐weighted eigenvalues of Sturm–Liouville equations with integrable potentials and an application to inverse problems

In this paper, we further Meirong Zhang et al.'s work by computing the number of weighted eigenvalues for Sturm–Liouville equations, equipped with general integrable potentials and Dirac weights, under Dirichlet boundary condition. We show that, for a Sturm–Liouville equation with a general integrable potential, if its weight is a positive linear combination of n Dirac delta functions, then it has at most n (may be less than n, or even be 0) distinct real Dirichlet eigenvalues, or every complex number is a Dirichlet eigenvalue; in particular, under some sharp condition, the number of Dirichlet eigenvalues is exactly n. Our main method is to introduce the concepts of characteristics matrix and characteristics polynomial for Sturm–Liouville problem with Dirac weights and put forward a general and direct algorithm used for computing eigenvalues. As an application, a class of inverse Dirichlet problems for Sturm–Liouville equations involving single Dirac distribution weights is studied.

Caputo fractional-order SEIRP model for COVID-19 Pandemic

We propose a Caputo-based fractional compartmental model for the dynamics of the novel COVID-19 pandemic. The newly proposed nonlinear fractional order model is an extension of a recently formulated integer-order COVID-19 mathematical model. Using basic concepts such as continuity and Banach fixed-point theorem, existence and uniqueness of the solution to the proposed model were shown. Furthermore, we analyze the stability of the model in the context of Ulam-Hyers and generalized Ulam-Hyers stability criteria. The concept of next-generation matrix was used to compute the basic reproduction number R0, a number that determines the spread or otherwise of the disease into the general population. We also investigated the local asymptotic stability for the derived disease-free equilibrium point. Numerical simulation of the constructed epidemic model was carried out using the fractional Adam-Bashforth-Moulton method to validate the obtained theoretical results.

A Novel Machine-Learning Framework-based on LBP and GLCM Approaches for CBIR System

This paper presents a Multiple-features extraction and reduction-based approaches for Content-Based Image Retrieval (CBIR). Discrete Wavelet Transforms (DWT) on colored channels is used to decompose the image at multiple stages. The Gray Level Co-occurrence Matrix (GLCM) concept is used to extract statistical characteristics for texture image classification. The definition of shared knowledge is used to classify the most common features for all COREL dataset groups. These are also fed into a feature selector based on the particle swarm optimization which reduces the number of features that can be used during the classification stage. Three classifiers, called the Support Vector Machine (SVM), K-Nearest Neighbor (KNN) and Decision Tree (DT), are trained and tested, in which SVM give high classification accuracy and precise rates. In several of the COREL dataset types, experimental findings have demonstrated above 94 percent precision and 0.80 to 0.90 precision values.

Unsteady aero-elastic analysis of a composite wing containing an edge crack

This paper deals with the investigation of the influence of edge surface crack on the flutter behavior of unidirectional fiber-reinforced composite wing subjected to unsteady aerodynamic loads. The cracked wing is modeled as a two-interconnected Euler–Bernoulli beam at the crack location, where the related crack is modeled using continuity conditions and the local flexibility matrix concept. The components of this matrix are extracted from the theory of linear fracture mechanics. The formulation takes into account the effects of bending-torsion coupling due to the unbalanced laminates and offset of the center of gravity inherent to composite structures. The fundamental modes of intact and cracked cantilevered beams, derived from the free vibration analysis by the dynamic stiffness matrix, are used in Galerkin's method. The modified shape functions are developed to reflect the crack effect in the aeroelastic analysis, wherein an unsteady aerodynamic model based on strip theory is employed. By a combination of structure and aerodynamic formulations and using the modified mode shapes and applying a new iteration algorithm, the flutter boundary is determined. Also, the procedure has been evaluated by solving the number of problems available in the literature. Then effects of various parameters, such as the fiber angle, the crack location, the crack length, and the aerodynamic model, on the flutter boundary are analyzed and a detailed discussion will be addressed. It was found that these parameters can have a positive or negative influence on the flutter behavior of the structure.

Nonlinear Vibration of a Time-Space Coupled Drill String System Based on the Surface Morphology of Rock

In this paper, the nonlinear vibration of a time-space coupled axial and torsional drill string system is investigated. Considering the surface morphology of rock, top drive system and mud, the drill string system is discretized by finite element method. The dynamic equations of the fully discrete drill string system based on rock surface morphology (SM) is established. Based on the surface morphology and strength of rock, the concept of rock surface state matrix is proposed. The stability and time domain response of the system are obtained by numerical simulation and compared with the multiple regeneration (MR) model. The results show that stick slip vibration and bit reversal are more likely to occur when drilling system cuts unhomogeneous rock, and stick slip vibration is the main reason to cause the drill bit impact rock. The stable driving torsional speed is lower than that of calculated by conventional models. In the calculation process, the volume conservation accuracy of the SM model is higher than that of the MR model. Moreover, the numerical convergence and efficiency of SM model are higher than that of MR model.

Matrix Formulation of EISs of Graphs and Its Application to WSN Covering Problems

In this paper, the problem of formulating and finding externally independent sets of graphs is considered by using a newly developed STP method, called semitensor product of matrices. By introducing a characteristic value of a vertex subset of a graph and using the algebraic representation of pseudological functions, several necessary and sufficient conditions of matrix form are proposed to express the externally independent sets (EISs), minimum externally independent sets (MEISs), and kernels of graphs. Based on this, the concepts of EIS matrix, MEIS matrix, and kernel matrix are introduced. By these matrices’ complete characterization of these three structures of graphs, three algorithms are further designed which can find all these kinds of subsets of graphs mathematically. The results are finally applied to a WSN covering problem to demonstrate the correctness and effectiveness of the proposed results.

Partial backlogging inventory model with price and stock level dependent demand, time varying holding cost and quantity discounts

This article deals with an increasing total profit for inventory optimal ordered quantity and partial backlogging with the holding cost depending on the storage time period, and the rate of market demand is assumed to fluctuate as a function, based on level of stock and selling price. Thereafter, using the concept of a Hessian matrix, we have proved the concave nature of the profit function for the case where maximum cost is obtained. Finally, in order to validate the derived models, numerical examples and sensitivity analysis are explained. Through numerical test, we show that the proposed algorithms give quite satisfactory solutions. Hence, it can be concluded that the total profit can be increased by allowing shortage and partial backlogging.

Inverse optimal control from incomplete trajectory observations

This article develops a methodology that enables learning an objective function of an optimal control system from incomplete trajectory observations. The objective function is assumed to be a weighted sum of features (or basis functions) with unknown weights, and the observed data is a segment of a trajectory of system states and inputs. The proposed technique introduces the concept of the recovery matrix to establish the relationship between any available segment of the trajectory and the weights of given candidate features. The rank of the recovery matrix indicates whether a subset of relevant features can be found among the candidate features and the corresponding weights can be learned from the segment data. The recovery matrix can be obtained iteratively and its rank non-decreasing property shows that additional observations may contribute to the objective learning. Based on the recovery matrix, a method for using incomplete trajectory observations to learn the weights of selected features is established, and an incremental inverse optimal control algorithm is developed by automatically finding the minimal required observation. The effectiveness of the proposed method is demonstrated on a linear quadratic regulator system and a simulated robot manipulator.

Extending the Capture Map Concept to Estimate Discrete and Risk-Based Streamflow Depletion Potential.

A popular and contemporary use of numerical groundwater models is to estimate the discrete relation between groundwater extraction and surface-water/groundwater exchange. Previously, the concept of a "capture map" has been put forward as a means to effectively summarize this relation for decision-making consumption. While capture maps have enjoyed success in the environmental simulation industry, they are deterministic, ignoring uncertainty in the underlying model. Furthermore, capture maps are not typically calculated in a manner that facilitates analysis of varying combinations of extraction locations and/or reaches. That is, they are typically constructed with focus on a single reach or group of reaches. The former of these limitations is important for conveying risk to decision makers and stakeholders, while the latter is important for decision-making support related to surface-water management, where future foci may include reaches that were not the focus of the original capture analysis. Herein, we use the concept of a response matrix to generalize the theory of the capture-map approach to estimate spatially discrete streamflow depletion potential. We also use first-order, second-moment uncertainty estimation techniques with the concept of "risk shifting" to place capture maps and streamflow depletion potential in a stochastic, risk-based framework. Our approach is demonstrated for an integrated groundwater/surface-water model of the lower San Antonio River, Texas, USA.

Ordinal citizenship.

The expansion of social citizenship in the 20th century mitigated the brute effects of economic inequality in people's lives. The new rights also created new social divisions, however, separating citizens according to their ability to do well through them. In the 21st century the conceptual matrix of citizenship has developed further, powered by new technologies that have promised new freedoms and opportunities in every aspect of people's lives. As the scope of economic and social incorporation has broadened, the possibilities for classifying, sorting, slotting, and scaling people have also grown and diversified. Echoing the earlier rise of the meritocracy, this new matrix produces its own winners and losers, partly recycling old inequalities, and partly creating new ones. Demands for self-care and individual fitness pile up, eroding the universal and solidaristic basis upon which the expansion of citizenship historically thrived. In its place stands what I call "ordinal citizenship," a form of social inclusion that thrives on social measurement, differentiation, and hierarchy.

The concept repentance in the structure of the cognitive matrix “christian moral values” and its verbalizers

The article deals with verbalizers of the phrasal concept REPENTANCE in the system of Christian moral values of the English language culture. In the proposed study, cognitive-matrix analysis was implemented as the main research methodology, the principles of which were developed by Yu. M. Boldyrev. It is based on the concept of matrix (nets) domains, in which the matrix can be illustrated graphically as a grid. It is understood as a simple set of conceptual areas, and the conceptual sphere or domain - as a context for updating the meaning of the word. The domains‟ matrix is identified in intelligence as a value system of Christianity verbalized through the system of biblical phraseology of American and British English. Scientific novelty. The exploration specifies the terminological scope of the term “biblical phraseology / biblical expression”; the essence of the method of cognitive-matrix analysis is shown, too. Conclusions. The analysis is underpinned by phraseographic sources and the conceptual component of the concept REPENTANCE has been characterized. This analysis has revealed the place of this linguistic essential quality in the structure of the integrative concept (matrix) of CHRISTIAN MORAL VALUES and the correlation of the concept of REPENTANCE with the domain of repentance is determined. The selected biblical expressions, verbalizers of this concept, are defined and characterized.

Peripheral arterial stiffness during electrocutaneous stimulation is positively correlated with pain-related brain activity and subjective pain intensity: an fMRI study

Brain activity associated with pain perception has been revealed by numerous PET and fMRI studies over the past few decades. These findings helped to establish the concept of the pain matrix, which is the distributed brain networks that demonstrate pain-specific cortical activities. We previously found that peripheral arterial stiffness {beta }_{text{art}} responds to pain intensity, which is estimated from electrocardiography, continuous sphygmomanometer, and photo-plethysmography. However, it remains unclear whether and to what extent {beta }_{text{art}} aligns with pain matrix brain activity. In this fMRI study, 22 participants received different intensities of pain stimuli. We identified brain regions in which the blood oxygen level-dependent signal covaried with {beta }_{text{art}} using parametric modulation analysis. Among the identified brain regions, the lateral and medial prefrontal cortex and ventral and dorsal anterior cingulate cortex were consistent with the pain matrix. We found moderate correlations between the average activities in these regions and {beta }_{text{art}} (r = 0.47, p < 0.001). {beta }_{text{art}} was also significantly correlated with self-reported pain intensity (r = 0.44, p < 0.001) and applied pain intensity (r = 0.43, p < 0.001). Our results indicate that {beta }_{text{art}} is positively correlated with pain-related brain activity and subjective pain intensity. This study may thus represent a basis for adopting peripheral arterial stiffness as an objective pain evaluation metric.

Performance Analysis of Feedback-Based Network-Coded Systems for Broadcast

In a broadcast transmission over an erasure network, feedback with network coding is both capacity-achieving and loss-immune. In this article, we carry out performance analyses of the feedback-based online network coding technique, drop when seen (DWS), and its recently proposed randomized variant (rDWS). An absorbing discrete time Markov chain (DTMC) model is constructed to find the probability of dropping a packet from the sender queue (even before decoding) in a generation-based DWS broadcast. The dropping probability is computed efficiently in homogeneous as well as in heterogeneous erasure scenario by a tensor-algebraic formulation on top of the DTMC model. Further, the notion of first time drop leads to obtain a dropping distribution. A similar inspection for rDWS is not straight-forward because of receivers’ Markov-state dependency. So, the analysis is carried out with respect to Independent Markov-state Model (IMM), and the model is shown to be accurate in most of the cases except the situations where erasure probabilities, number of receivers, field size, target time slot all are very low. Another characterization of the dropping phenomenon helps in establishing the fact, average dropping time strictly decreases with generation size for DWS , and we conjecture, the same holds for rDWS. Using the fundamental matrix concept, we calculate the mean decoding time of a generation for a receiver. Extending the idea of first time dropping to decoding, statistics of different decoding options are analyzed. Finally, some analytical and simulation plots yield, the light-weight rDWS exhibits a very close performance to DWS for a sufficiently large finite field.

Content Independent Location Based Clustering for 5G Device to Device Communications

In this paper we have addressed a content independent location based clustering technique for fifth generation device-to-device (D2D) communications. Our objective is to serve a suitable number of requesting D2D pairs through an overlay cluster based communication irrespective of their content. To do so we have described a framework for the proposed approach addressing the required parameters. We then developed an analytical model of a novel cluster-head selection strategy using the concept of sparse matrix. Based on these, a location based cluster formation (LBCF) algorithm has been designed for maximizing the service coverage taking care of the inter-cluster interference through proper power tuning and appropriate resource allocation. Extensive simulations have been performed using network simulator 2 for the evaluation of our proposed LBCF approach. It has been shown that LBCF confirms notable service coverage and achieves desirable throughput in comparison to a non-cluster approach. The efficiency of resource utilization is also established. Simulation results show that the proposed approach is efficient enough to provide uniform signal coverage to the members of the same cluster and gives a comparable performance with other existing approaches. Finally the novelty of the proposed LBCF is established through a sensitivity analysis.

Development of a hybrid framework for inventory leanness in Technical Services Organizations.

Inherent uncertainties in demand and supply make it problematic for supply chains to accomplish optimum inventory replenishment, resulting in loss of sales or keeping excessive inventories. To cope with erratic demands, organizations have to maintain excessive inventory levels, sometimes taking up to one-third of an organization’s annual budget. The two most pressing concerns to handle in inventory management are: how much to order and when to order. Therefore, an organization ought to make the correct and timely decisions based on precise demand information to avoid excessive inventory accumulation resulting in enhanced competitive advantage. Owing to the significance of inventory control and analysis, this paper reports on developing and successfully implementing a hybrid framework for optimum level inventory forecasting in Technical Services Organizations. The proposed framework is based on a case study of one of Pakistan’s leading Technical Services Organization. The paper presents a statistical analysis of historical data and a comprehensive fault trend analysis. Both these analyses set a solid foundation for the formulation of a comparative analysis matrix based upon price and quantity based analysis of inventory. Finally, a decision criterion (Forecasting Model) is proposed using three primary forecasting techniques with minimum error calculations. The study’s finding shows a forecast error of 142.5 million rupees in the last five years, resulting in the accumulation of more than 25 thousand excessive inventory stock. Application of price and quantity based analysis identifies that 65% of the annual budget is significantly dependent upon only 9% (in terms of quantity) of "High Price and Small Quantity" Items (HS). These HS items are forecasted through three different forecasting methods, i.e., Weighted Moving Average, Exponential Smoothing, and Trend Projection, with Minimum Absolute Deviation to significantly reduce the forecasting error while predicting the future required quantity. The research work aims to contribute to the inventory management literature in three ways. First, a new comparative analysis matrix concept for identifying the most critical items is introduced. Second, a Multi-Criteria Forecasting Model is developed to capture a wide range of operations. Third, the paper suggests how these forecasting criteria can be integrated into a single interactive DSS to maintain optimum inventory level stock. Even though the DSS framework is based on data from a single organization, the application is expected to manage inventory stock in a wide range of manufacturing and services industries. This study’s proposed hybrid framework is the first of its kind that encapsulates all four dimensions of inventory classification criteria, forming a multi-criteria hybrid model within a DSS framework.

Stability assessment of a stand-alone wind-photovoltaic-battery system via Floquet Theory

This paper presents a methodology, based on both Floquet theory and the participation matrix concepts, aimed at characterization of a time-periodic system in terms of its poles location in the complex plane. The participation matrix allows to find which poles are the most influenced by certain state-variables. The proposed methodology can be utilized as an auxiliary tool for parameter design, stability assessment, and for post-event analysis of time-periodic systems. The proposed methodology is readily applicable to distributed generation systems. A case study involving a stand-alone wind-photovoltaic-battery system is presented to support this statement.

Modeling the Mechanobiology of Cancer Cell Migration Using 3D Biomimetic Hydrogels.

Understanding how cancer cells migrate, and how this migration is affected by the mechanical and chemical composition of the extracellular matrix (ECM) is critical to investigate and possibly interfere with the metastatic process, which is responsible for most cancer-related deaths. In this article we review the state of the art about the use of hydrogel-based three-dimensional (3D) scaffolds as artificial platforms to model the mechanobiology of cancer cell migration. We start by briefly reviewing the concept and composition of the extracellular matrix (ECM) and the materials commonly used to recreate the cancerous ECM. Then we summarize the most relevant knowledge about the mechanobiology of cancer cell migration that has been obtained using 3D hydrogel scaffolds, and relate those discoveries to what has been observed in the clinical management of solid tumors. Finally, we review some recent methodological developments, specifically the use of novel bioprinting techniques and microfluidics to create realistic hydrogel-based models of the cancer ECM, and some of their applications in the context of the study of cancer cell migration.

Digital communication, value co-creation and customer engagement in business networks: a conceptual matrix and propositions

PurposeTechnological innovations that resulted in the emergence and widespread adoption of digital communication in recent years have led to a surge of academic and practitioner interest in its implications for the co-creation of value and customer engagement. However, in comparison to the attention given to the study of customer engagement in consumer markets, few studies have examined its key role in business markets. This paper aims to examine the impact of digital communication on value co-creation and customer engagement in inter-organizational relationships in business networks.Design/methodology/approachCo-creation of value and customer engagement in business networks occurs among interconnected organizations that are partners in intermediate transactions. The paper develops a matrix of inter-organizational engagement among partners in business networks and propositions linking digital communication to value co-creation and inter-organizational engagement.FindingsThe relationships among network organizations may be characterized by the extent of relational exchange and inter-organizational bonds among them. Four types of inter-organizational engagement emerge: transactional partners, loyal partners, trusted partners and engaged partners. The partners co-create value to better satisfy customers.Research limitations/implicationsThe paper is an initial attempt to develop a conceptual understanding of customer engagement in business markets and formulate propositions that can be further investigated. Networks of partner organizations co-create value, altering their input and output markets, value addition and products, permitting greater flexibility and customization in satisfying the needs of customers.Practical implicationsThe ability afforded by digital communication for real-time interactive communication enables individuals from multiple departments and hierarchical positions within multiple organizations dispersed across geographic locations and industries to maintain contact, quickly and easily communicate task information, build trust and commitment in long-term relationships with network partners and provide superior customer value.Originality/valueThe paper represents a unique attempt to understand the nature of customer engagement in business markets. It discusses how digital communication alters market transactions among partner organizations in a network by facilitating changes in their make/buy decisions. It develops a matrix of inter-organizational engagement in business networks and propositions that improve understanding of the customer engagement concept and provide the foundation for strategies to better satisfy customers.

Decision making using new category of similarity measures and study their applications in medical diagnosis problems

The aim of this paper is to propose a new category of similarity measures, we begin to introduce the concept of effect matrix $$\mathop T\limits^{ \wedge } (R_{1} \times R_{2} \times R_{3} ,p_{m} ,q_{n} ,f_{v} )$$ of type 3-tuple and study some of their properties. Moreover, from the soft set we find the pictures of type regular and irregular using effect matrix $$\mathop T\limits^{ \wedge } (R_{1} \times R_{2} \times R_{3} ,p_{m} ,q_{n} ,f_{v} )$$ of type 3-tuple are found. An effect matrix $$\mathop T\limits^{ \wedge } (R_{1} \times R_{2} \times R_{3} ,p_{m} ,q_{n} ,f_{v} )$$ of type 3-tuple is better than effect matrix $$\mathop T\limits^{ \wedge } (\Re_{1} \times \Re_{2} ,p_{n} ,q_{m} )$$ of type 2-tuple, because we can deal with three different sets $$R_{1}$$ (a family of objectives), $$R_{2}$$ (a family of parameters), $$R_{3}$$ (a family of second parameters) in the same problem. This burden can be alleviated by application of type 3-tuple. Some applications of soft effect matrix of type 3-tuple $$\mathop T\limits^{ \wedge } (R_{1} \times R_{2} \times R_{3} ,p_{m} ,q_{n} ,f_{v} )$$ in decision making problems are studied and explained. In this work we deal with pictures. Moreover, the similarity measure between two different soft sets under the same universal soft set $$(R_{1} \times R_{2} \times R_{3} )$$ can be studied and explained its applications in medical diagnosis problems.