Pupil dynamics are the important characteristics of face spoofing detection.The face recognition system is one of the most used biometrics for authenticating individual identity.The main threats to the facial recognit...Pupil dynamics are the important characteristics of face spoofing detection.The face recognition system is one of the most used biometrics for authenticating individual identity.The main threats to the facial recognition system are different types of presentation attacks like print attacks,3D mask attacks,replay attacks,etc.The proposed model uses pupil characteristics for liveness detection during the authentication process.The pupillary light reflex is an involuntary reaction controlling the pupil’s diameter at different light intensities.The proposed framework consists of two-phase methodologies.In the first phase,the pupil’s diameter is calculated by applying stimulus(light)in one eye of the subject and calculating the constriction of the pupil size on both eyes in different video frames.The above measurement is converted into feature space using Kohn and Clynes model-defined parameters.The Support Vector Machine is used to classify legitimate subjects when the diameter change is normal(or when the eye is alive)or illegitimate subjects when there is no change or abnormal oscillations of pupil behavior due to the presence of printed photograph,video,or 3D mask of the subject in front of the camera.In the second phase,we perform the facial recognition process.Scale-invariant feature transform(SIFT)is used to find the features from the facial images,with each feature having a size of a 128-dimensional vector.These features are scale,rotation,and orientation invariant and are used for recognizing facial images.The brute force matching algorithm is used for matching features of two different images.The threshold value we considered is 0.08 for good matches.To analyze the performance of the framework,we tested our model in two Face antispoofing datasets named Replay attack datasets and CASIA-SURF datasets,which were used because they contain the videos of the subjects in each sample having three modalities(RGB,IR,Depth).The CASIA-SURF datasets showed an 89.9%Equal Error Rate,while the Replay Attack datasets showed a 92.1%Equal Error Rate.展开更多
This study outlines the essential nursing strategies employed in the care of 10 patients experiencing vascular vagal reflex, managed with artificial liver support systems. It highlights a holistic nursing approach tai...This study outlines the essential nursing strategies employed in the care of 10 patients experiencing vascular vagal reflex, managed with artificial liver support systems. It highlights a holistic nursing approach tailored to the distinct clinical manifestations of these patients. Key interventions included early detection of psychological issues prior to initiating treatment, the implementation of comprehensive health education, meticulous monitoring of vital signs throughout the therapy, prompt emergency interventions when needed, adherence to prescribed medication protocols, and careful post-treatment observations including venous catheter management. Following rigorous treatment and dedicated nursing care, 7 patients demonstrated significant improvement and were subsequently discharged.展开更多
Hepatitis D virus(HDV)can infect HBsAg-positive individuals,causing rapid fibrosis progression,early decompensation,increased hepatocellular carcinoma risk,and higher mortality than hepatitis B virus(HBV)mono-infectio...Hepatitis D virus(HDV)can infect HBsAg-positive individuals,causing rapid fibrosis progression,early decompensation,increased hepatocellular carcinoma risk,and higher mortality than hepatitis B virus(HBV)mono-infection.Most countries lack high-quality HDV prevalence data,and the collection techniques employed often bias published data.In recent meta-analyses,HDV prevalence in HBsAg-positive patients reaches 5%-15%and is even significantly higher in endemic areas.Since HBV vaccination programs were implemented,HDV prevalence has decreased among younger populations.However,owing to immigrant influx,it has increased in some Western countries.The current practice of HDV screening in HBsAg-positive individuals is stepwise,based on physician’s discretion,and limited to at-risk populations and may require numerous visits.Double reflex testing,which includes anti-HDV testing in all HBsAg-positive individuals and then HDV RNA testing for anti-HDV-positive ones,is uncommon.Reflex testing can identify more HDV infection cases and link identified patients to further care and follow-up.Moreover,laboratory-based double reflex screening is less biased than physician-led testing.Therefore,health-care providers should learn about reflex testing,and federal and provincial hepatitis control programs should implement laboratory-based double reflex testing to obtain reliable HDV prevalence estimates.The test’s cost-effectiveness depends on the number of HBV-positive patients screened to identify one HDV-positive patient.Such testing may be viable in areas with low HBsAg but high HDV prevalence.However,its economic impact on areas with low HDV prevalence needs further study.展开更多
In this article, the generalized reflexive solution of matrix equations (AX = B, XC = D) is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solv...In this article, the generalized reflexive solution of matrix equations (AX = B, XC = D) is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.展开更多
We derive necessary and sufficient conditions for the existence and an expression of the (anti)reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equati...We derive necessary and sufficient conditions for the existence and an expression of the (anti)reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ||X - E||F was given, where E is a given complex matrix and Ф is the set of all reflexive (or antireflexive) solutions of the system mentioned above, and ||·|| is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.展开更多
This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces. A necessary and sufficient condition for approximate controllability via L^p([0, T...This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces. A necessary and sufficient condition for approximate controllability via L^p([0, T], U), 1≤p〈∞ is obtained,where L^p( [0, T], U) is the control function space.展开更多
Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive...Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive) if PXP = X(P XP =-X). The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.展开更多
In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solu...In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.展开更多
A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalize...A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems (SAGMEPs) for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.展开更多
The matrix equations (AX, XBH)=(C, DH) have been widely used in structural design, parameter identification, linear optimal control, and so on. But few researches studied the reflexive solutions. A new approach for th...The matrix equations (AX, XBH)=(C, DH) have been widely used in structural design, parameter identification, linear optimal control, and so on. But few researches studied the reflexive solutions. A new approach for the reflexive solutions to the matrix equations was proposed. By applying the canonical correlation decomposition (CCD) of matrix pairs, the necessary and sufficient conditions for the existence and the general expression for the reflexive solutions of the matrix equations (AX, XBH)=(C, DH) were established. In addition, by using the methods of space decomposition, the expression of the optimal approximation solution to a given matrix was derived.展开更多
A new bilevel generalized mixed equilibrium problem (BGMEP) involving generalized mixed variational-like inequality problems (GMVLIPs) is introduced and studied in the reflexive Banach spaces. First, an auxiliary ...A new bilevel generalized mixed equilibrium problem (BGMEP) involving generalized mixed variational-like inequality problems (GMVLIPs) is introduced and studied in the reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs. By using a minimax inequality, the existence and the unique- ness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions. By using an auxiliary principle technique, the new iterative algorithms are proposed and analyzed, with which the approximate solutions of the BGMEP are computed. The strong convergence of the iterative sequence generated by the algorithms is shown under mild conditions without any coercive assumptions. These new results can generalize some recent results in this field.展开更多
Generalize reflexive matrices are a special class of matrices ?that have the relation where? and ?are some generalized reflection matrices. The nontrivial cases ( or ) of this class of matrices occur very often in man...Generalize reflexive matrices are a special class of matrices ?that have the relation where? and ?are some generalized reflection matrices. The nontrivial cases ( or ) of this class of matrices occur very often in many scientific and engineering applications. They are also a generalization of centrosymmetric matrices and reflexive matrices. The main purpose of this paper is to present block decomposition schemes for generalized reflexive matrices of various types and to obtain their decomposed explicit block-diagonal structures. The decompositions make use of unitary equivalence transformations and, therefore, preserve the singular values of the matrices. They lead to more efficient sequential computations and at the same time induce large-grain parallelism as a by-product, making themselves computationally attractive for large-scale applications. A numerical example is employed to show the usefulness of the developed explicit decompositions for decoupling linear least-square problems whose coefficient matrices are of this class into smaller and independent subproblems.展开更多
Among the huge diversity of ideas that show up while studying graph theory,one that has obtained a lot of popularity is the concept of labelings of graphs.Graph labelings give valuable mathematical models for a wide s...Among the huge diversity of ideas that show up while studying graph theory,one that has obtained a lot of popularity is the concept of labelings of graphs.Graph labelings give valuable mathematical models for a wide scope of applications in high technologies(cryptography,astronomy,data security,various coding theory problems,communication networks,etc.).A labeling or a valuation of a graph is any mapping that sends a certain set of graph elements to a certain set of numbers subject to certain conditions.Graph labeling is a mapping of elements of the graph,i.e.,vertex and for edges to a set of numbers(usually positive integers),called labels.If the domain is the vertex-set or the edge-set,the labelings are called vertex labelings or edge labelings respectively.Similarly,if the domain is V(G)[E(G)],then the labeling is called total labeling.A reflexive edge irregular k-labeling of graph introduced by Tanna et al.:A total labeling of graph such that for any two different edges ab and a'b'of the graph their weights has wt_(x)(ab)=x(a)+x(ab)+x(b) and wt_(x)(a'b')=x(a')+x(a'b')+x(b') are distinct.The smallest value of k for which such labeling exist is called the reflexive edge strength of the graph and is denoted by res(G).In this paper we have found the exact value of the reflexive edge irregularity strength of the categorical product of two paths (P_(a)×P_(b))for any choice of a≥3 and b≥3.展开更多
Let S∈Rn×n be a symmetric and nontrival involution matrix. We say that A∈E R n×n is a symmetric reflexive matrix if AT = A and SAS = A. Let S R r n×n(S)={A|A= AT,A = SAS, A∈Rn×n}. This paper dis...Let S∈Rn×n be a symmetric and nontrival involution matrix. We say that A∈E R n×n is a symmetric reflexive matrix if AT = A and SAS = A. Let S R r n×n(S)={A|A= AT,A = SAS, A∈Rn×n}. This paper discusses the following two problems. The first one is as follows. Given Z∈Rn×m (m < n),∧= diag(λ1,...,λm)∈Rm×m, andα,β∈R withα<β. Find a subset (?)(Z,∧,α,β) of SRrn×n(S) such that AZ = Z∧holds for any A∈(?)(Z,∧,α,β) and the remaining eigenvaluesλm+1 ,...,λn of A are located in the interval [α,β], Moreover, for a given B∈Rn×n, the second problem is to find AB∈(?)(Z,∧,α,β) such that where ||.|| is the Frobenius norm. Using the properties of symmetric reflexive matrices, the two problems are essentially decomposed into the same kind of subproblems for two real symmetric matrices with smaller dimensions, and then the expressions of the general solution for the two problems are derived.展开更多
Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the ex...Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the extreme ranks of the real matrices. As applications, we establish necessary and sufficient conditions for some special least-squares g-inverse and minimum norm g-inverse.展开更多
Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized p...Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.展开更多
The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on rea...The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see <a href="#ref1">[1]</a> <a href="#ref2">[2]</a> <a href="#ref3">[3]</a>. We then consider a linear FS <img src="Edit_4629d4d0-bbb2-478d-adde-391efde3d1e0.bmp" alt="" />, and prove that, if <img src="Edit_435aae08-e821-4b4d-99d2-e2a2b47609c1.bmp" alt="" />;<img src="Edit_4fa030bc-1f97-4726-8257-ca8d00657aac.bmp" alt="" /> , with <img src="Edit_63ab4faa-ba40-45fe-8b8a-7a6caef91794.bmp" alt="" />the respective solutions of FS’s [A,B] and <img src="Edit_e78e2e6d-8934-4011-93eb-8b7eb52fa856.bmp" alt="" /> corresponding to the given (u,v) in <img src="Edit_0e18433c-8c7a-454f-8eec-6eb9fb69469a.bmp" alt="" /> . There exists,<img src="Edit_3dcd8afc-8cea-4c06-a920-e4148a5f793e.bmp" alt="" />, positive real constants such that, <img src="Edit_edb88446-3e39-4fe0-865a-114de701e78e.bmp" alt="" />. These results are the subject of theorems 3.1, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.3. The proofs of these theorems are based on our lemmas 3.2, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator <em>I+BA</em> and <img src="Edit_2db1326b-cb5b-44cf-8d1f-df22bd6da45f.bmp" alt="" />. The results obtained and demonstrated along this document, present an extension in general Banach space of those in <a href="#ref4">[4]</a> on a Hilbert space <em>H</em> and those in <a href="#ref5">[5]</a> on a extended Hilbert space <img src="Edit_b70ce337-1812-4d4b-ae7d-a24da7e5b3cf.bmp" alt="" />.展开更多
基金funded by Researchers Supporting Program at King Saud University (RSPD2023R809).
文摘Pupil dynamics are the important characteristics of face spoofing detection.The face recognition system is one of the most used biometrics for authenticating individual identity.The main threats to the facial recognition system are different types of presentation attacks like print attacks,3D mask attacks,replay attacks,etc.The proposed model uses pupil characteristics for liveness detection during the authentication process.The pupillary light reflex is an involuntary reaction controlling the pupil’s diameter at different light intensities.The proposed framework consists of two-phase methodologies.In the first phase,the pupil’s diameter is calculated by applying stimulus(light)in one eye of the subject and calculating the constriction of the pupil size on both eyes in different video frames.The above measurement is converted into feature space using Kohn and Clynes model-defined parameters.The Support Vector Machine is used to classify legitimate subjects when the diameter change is normal(or when the eye is alive)or illegitimate subjects when there is no change or abnormal oscillations of pupil behavior due to the presence of printed photograph,video,or 3D mask of the subject in front of the camera.In the second phase,we perform the facial recognition process.Scale-invariant feature transform(SIFT)is used to find the features from the facial images,with each feature having a size of a 128-dimensional vector.These features are scale,rotation,and orientation invariant and are used for recognizing facial images.The brute force matching algorithm is used for matching features of two different images.The threshold value we considered is 0.08 for good matches.To analyze the performance of the framework,we tested our model in two Face antispoofing datasets named Replay attack datasets and CASIA-SURF datasets,which were used because they contain the videos of the subjects in each sample having three modalities(RGB,IR,Depth).The CASIA-SURF datasets showed an 89.9%Equal Error Rate,while the Replay Attack datasets showed a 92.1%Equal Error Rate.
文摘This study outlines the essential nursing strategies employed in the care of 10 patients experiencing vascular vagal reflex, managed with artificial liver support systems. It highlights a holistic nursing approach tailored to the distinct clinical manifestations of these patients. Key interventions included early detection of psychological issues prior to initiating treatment, the implementation of comprehensive health education, meticulous monitoring of vital signs throughout the therapy, prompt emergency interventions when needed, adherence to prescribed medication protocols, and careful post-treatment observations including venous catheter management. Following rigorous treatment and dedicated nursing care, 7 patients demonstrated significant improvement and were subsequently discharged.
文摘Hepatitis D virus(HDV)can infect HBsAg-positive individuals,causing rapid fibrosis progression,early decompensation,increased hepatocellular carcinoma risk,and higher mortality than hepatitis B virus(HBV)mono-infection.Most countries lack high-quality HDV prevalence data,and the collection techniques employed often bias published data.In recent meta-analyses,HDV prevalence in HBsAg-positive patients reaches 5%-15%and is even significantly higher in endemic areas.Since HBV vaccination programs were implemented,HDV prevalence has decreased among younger populations.However,owing to immigrant influx,it has increased in some Western countries.The current practice of HDV screening in HBsAg-positive individuals is stepwise,based on physician’s discretion,and limited to at-risk populations and may require numerous visits.Double reflex testing,which includes anti-HDV testing in all HBsAg-positive individuals and then HDV RNA testing for anti-HDV-positive ones,is uncommon.Reflex testing can identify more HDV infection cases and link identified patients to further care and follow-up.Moreover,laboratory-based double reflex screening is less biased than physician-led testing.Therefore,health-care providers should learn about reflex testing,and federal and provincial hepatitis control programs should implement laboratory-based double reflex testing to obtain reliable HDV prevalence estimates.The test’s cost-effectiveness depends on the number of HBV-positive patients screened to identify one HDV-positive patient.Such testing may be viable in areas with low HBsAg but high HDV prevalence.However,its economic impact on areas with low HDV prevalence needs further study.
基金supported by National Natural Science Foundation of China (10571047)and by Scientific Research Fund of Hunan Provincial Education Department of China Grant(06C235)+1 种基金by Central South University of Forestry and Technology (06Y017)by Specialized Research Fund for the Doctoral Program of Higher Education (20060532014)
文摘In this article, the generalized reflexive solution of matrix equations (AX = B, XC = D) is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.
基金supported by the National Natural Science Foundation of China (Grant No.60672160)
文摘We derive necessary and sufficient conditions for the existence and an expression of the (anti)reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ||X - E||F was given, where E is a given complex matrix and Ф is the set of all reflexive (or antireflexive) solutions of the system mentioned above, and ||·|| is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.
文摘This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces. A necessary and sufficient condition for approximate controllability via L^p([0, T], U), 1≤p〈∞ is obtained,where L^p( [0, T], U) is the control function space.
基金Supported by the Education Department Foundation of Hebei Province(QN2015218) Supported by the Natural Science Foundation of Hebei Province(A2015403050)
文摘Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive) if PXP = X(P XP =-X). The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.
文摘In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.
基金supported by the Scientific Research Fund of Sichuan Normal University (No.09ZDL04)the Sichuan Province Leading Academic Discipline Project (No.SZD0406)
文摘A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems (SAGMEPs) for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.
基金National Natural Science Foundation of China ( No. 60875007)
文摘The matrix equations (AX, XBH)=(C, DH) have been widely used in structural design, parameter identification, linear optimal control, and so on. But few researches studied the reflexive solutions. A new approach for the reflexive solutions to the matrix equations was proposed. By applying the canonical correlation decomposition (CCD) of matrix pairs, the necessary and sufficient conditions for the existence and the general expression for the reflexive solutions of the matrix equations (AX, XBH)=(C, DH) were established. In addition, by using the methods of space decomposition, the expression of the optimal approximation solution to a given matrix was derived.
基金Project supported by the Scientific Research Fund of Sichuan Normal University(No.09ZDL04)the Leading Academic Discipline Project of Sichuan Province of China(No.SZD0406)
文摘A new bilevel generalized mixed equilibrium problem (BGMEP) involving generalized mixed variational-like inequality problems (GMVLIPs) is introduced and studied in the reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs. By using a minimax inequality, the existence and the unique- ness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions. By using an auxiliary principle technique, the new iterative algorithms are proposed and analyzed, with which the approximate solutions of the BGMEP are computed. The strong convergence of the iterative sequence generated by the algorithms is shown under mild conditions without any coercive assumptions. These new results can generalize some recent results in this field.
文摘Generalize reflexive matrices are a special class of matrices ?that have the relation where? and ?are some generalized reflection matrices. The nontrivial cases ( or ) of this class of matrices occur very often in many scientific and engineering applications. They are also a generalization of centrosymmetric matrices and reflexive matrices. The main purpose of this paper is to present block decomposition schemes for generalized reflexive matrices of various types and to obtain their decomposed explicit block-diagonal structures. The decompositions make use of unitary equivalence transformations and, therefore, preserve the singular values of the matrices. They lead to more efficient sequential computations and at the same time induce large-grain parallelism as a by-product, making themselves computationally attractive for large-scale applications. A numerical example is employed to show the usefulness of the developed explicit decompositions for decoupling linear least-square problems whose coefficient matrices are of this class into smaller and independent subproblems.
文摘Among the huge diversity of ideas that show up while studying graph theory,one that has obtained a lot of popularity is the concept of labelings of graphs.Graph labelings give valuable mathematical models for a wide scope of applications in high technologies(cryptography,astronomy,data security,various coding theory problems,communication networks,etc.).A labeling or a valuation of a graph is any mapping that sends a certain set of graph elements to a certain set of numbers subject to certain conditions.Graph labeling is a mapping of elements of the graph,i.e.,vertex and for edges to a set of numbers(usually positive integers),called labels.If the domain is the vertex-set or the edge-set,the labelings are called vertex labelings or edge labelings respectively.Similarly,if the domain is V(G)[E(G)],then the labeling is called total labeling.A reflexive edge irregular k-labeling of graph introduced by Tanna et al.:A total labeling of graph such that for any two different edges ab and a'b'of the graph their weights has wt_(x)(ab)=x(a)+x(ab)+x(b) and wt_(x)(a'b')=x(a')+x(a'b')+x(b') are distinct.The smallest value of k for which such labeling exist is called the reflexive edge strength of the graph and is denoted by res(G).In this paper we have found the exact value of the reflexive edge irregularity strength of the categorical product of two paths (P_(a)×P_(b))for any choice of a≥3 and b≥3.
基金Research supported by the National Natural Science Foundation of China. (10571047)
文摘Let S∈Rn×n be a symmetric and nontrival involution matrix. We say that A∈E R n×n is a symmetric reflexive matrix if AT = A and SAS = A. Let S R r n×n(S)={A|A= AT,A = SAS, A∈Rn×n}. This paper discusses the following two problems. The first one is as follows. Given Z∈Rn×m (m < n),∧= diag(λ1,...,λm)∈Rm×m, andα,β∈R withα<β. Find a subset (?)(Z,∧,α,β) of SRrn×n(S) such that AZ = Z∧holds for any A∈(?)(Z,∧,α,β) and the remaining eigenvaluesλm+1 ,...,λn of A are located in the interval [α,β], Moreover, for a given B∈Rn×n, the second problem is to find AB∈(?)(Z,∧,α,β) such that where ||.|| is the Frobenius norm. Using the properties of symmetric reflexive matrices, the two problems are essentially decomposed into the same kind of subproblems for two real symmetric matrices with smaller dimensions, and then the expressions of the general solution for the two problems are derived.
文摘Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the extreme ranks of the real matrices. As applications, we establish necessary and sufficient conditions for some special least-squares g-inverse and minimum norm g-inverse.
文摘Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.
文摘The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see <a href="#ref1">[1]</a> <a href="#ref2">[2]</a> <a href="#ref3">[3]</a>. We then consider a linear FS <img src="Edit_4629d4d0-bbb2-478d-adde-391efde3d1e0.bmp" alt="" />, and prove that, if <img src="Edit_435aae08-e821-4b4d-99d2-e2a2b47609c1.bmp" alt="" />;<img src="Edit_4fa030bc-1f97-4726-8257-ca8d00657aac.bmp" alt="" /> , with <img src="Edit_63ab4faa-ba40-45fe-8b8a-7a6caef91794.bmp" alt="" />the respective solutions of FS’s [A,B] and <img src="Edit_e78e2e6d-8934-4011-93eb-8b7eb52fa856.bmp" alt="" /> corresponding to the given (u,v) in <img src="Edit_0e18433c-8c7a-454f-8eec-6eb9fb69469a.bmp" alt="" /> . There exists,<img src="Edit_3dcd8afc-8cea-4c06-a920-e4148a5f793e.bmp" alt="" />, positive real constants such that, <img src="Edit_edb88446-3e39-4fe0-865a-114de701e78e.bmp" alt="" />. These results are the subject of theorems 3.1, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.3. The proofs of these theorems are based on our lemmas 3.2, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator <em>I+BA</em> and <img src="Edit_2db1326b-cb5b-44cf-8d1f-df22bd6da45f.bmp" alt="" />. The results obtained and demonstrated along this document, present an extension in general Banach space of those in <a href="#ref4">[4]</a> on a Hilbert space <em>H</em> and those in <a href="#ref5">[5]</a> on a extended Hilbert space <img src="Edit_b70ce337-1812-4d4b-ae7d-a24da7e5b3cf.bmp" alt="" />.