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We design several real representations of split quaternion matrices with the primary objective of establishing both necessary and sufficient conditions for the existence of solutions within a system of split quaternion matrix equations. This includes conditions for the general solution without any constraints, as well as X = ± X η solutions and η -(anti-)Hermitian solutions. Furthermore, we derive the expressions for the general solutions when it is solvable. As an application, we investigate the solutions to a system of five split quaternion matrix equations involving X ⋆ . Finally, we present several algorithms and numerical examples to demonstrate the results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Chen and Moore determinants of quaternion Hermitian matrices to dual quaternion Hermitian matrices. We show the Chen determinant of dual quaternion Hermitian matrices is invariant under addition, switching, multiplication, and unitary operations at the both hand sides. We then show the Chen and Moore determinants of dual quaternion Hermitian matrices are equal to each other, and they are also equal to the products of eigenvalues. The characteristic polynomial of a dual quaternion Hermitian matrix is also studied. [ABSTRACT FROM AUTHOR]

In this paper, we consider the solvability conditions of some Sylvester-type quaternion matrix equations. We establish some practical necessary and sufficient conditions for the existence of solutions of a Sylvester-type quaternion matrix equation with five unknowns through the corresponding equivalence relations of the block matrices. Moreover, we present some solvability conditions to some Sylvester-type quaternion matrix equations, including those involving Hermicity. The findings of this article extend related known results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of tensor least squares problem with an invertible linear transform, which arises in image restoration. Based on the operator-bidiagonal procedure, two Paige’s algorithms are designed to solve it. The convergence theorems of the new methods are derived. Numerical experiments are performed to illustrate the feasibility and efficiency of the new methods, including when the algorithm is tested with the synthetic data and on some image restoration problems. Comparisons with some previous methods are also given. [ABSTRACT FROM AUTHOR]

In Zhu et al. (Linear Multilinear Algebra 71:528–544, 2023), the authors described the left w-core inverse by principal ideals in ∗ -ring, and asked whether it can be defined by the solution of equations. In this paper, we answer the question in the positive. For any ∗ -ring R and a , w ∈ R , the element a is called left w-core invertible if there is some x ∈ R satisfying a w x a = a , x a w a = a and (a w x) ∗ = a w x . Several criteria for left w-core inverses are presented. Among of these, it is proved that a is left w-core invertible if and only if w is left invertible along a, a (or aw) is { 1 , 3 } -invertible and a ∈ a w R . Also, the relations among left w-core inverses, w-core inverses, and other generalized inverses are established. As applications, several characterizations for the Moore–Penrose inverse, the core inverse, and the pseudo-core inverse are given. [ABSTRACT FROM AUTHOR]

In this paper, we establish some necessary and sufficient conditions for the solvability to a system of five quaternion matrix equations in terms of the Moore–Penrose inverse and the rank of a matrix, and give an expression of the general solution to the system when it is consistent. As an application, we investigate an η -Hermicity solution of a system. Moreover, we present a numerical example to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we establish some necessary and sufficient conditions for the solvability to a system of two-sided Sylvester-like tensor equations over the quaternion algebra. We also construct an expression of the general solution to the system when it is solvable. As an application, we give some solvability conditions and expressions of the η -Hermitian solutions to some systems of two-sided Sylvester-like quaternion tensor equations. We also provide some algorithms and numerical examples to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

Mutual information of quantum channel is a natural extension of a basic concept in quantum information theory that of measuring the correlation of a composite quantum state. We first propose the mutual information of quantum channel based on max-relative entropy in multiple ways. We find that these quantities obey the data processing inequality under the action of superchannel. The super-additivity of mutual max-information of quantum channel is studied. Then, we investigate the corresponding smooth versions of mutual max-information of quantum channel, which also obey the data processing inequality under superchannel. We derive consistent lower and upper bounds for different one-shot testing channel , s mutual max-information in terms of the mutual information of output state through such channel. Furthermore, these bounds allow us to provide an alternative approach to prove the asymptotic equipartition property (AEP) for quantum channel , s smooth mutual max-information. Finally, by using this AEP, we obtain a channel version of the quantum Stein's lemma when discriminating between a large number of independent arbitrary channels and some special replacer channels. [ABSTRACT FROM AUTHOR]

This paper studies a system of three Sylvester-type quaternion matrix equations with ten variables A i X i + Y i B i + C i Z i D i + F i Z i + 1 G i = E i , i = 1 , 3 ¯ . We derive some necessary and sufficient conditions for the existence of a solution to this system in terms of ranks and Moore-Penrose inverses of the matrices involved. We present the general solution to the system when the solvability conditions are satisfied. As applications of this system, we provide some solvability conditions and general solutions to some systems of quaternion matrix equations involving ϕ-Hermicity. Moreover, we give some numerical examples to illustrate our results. The findings of this paper extend some known results in the literature. [ABSTRACT FROM AUTHOR]

The class of quaternion matrix optimization (QMO) problems, with quaternion matrices as decision variables, has been widely used in color image processing and other engineering areas in recent years. However, optimization theory for QMO is far from adequate. The main objective of this paper is to provide necessary theoretical foundations on optimality analysis, in order to enrich the contents of optimization theory and to pave way for the design of efficient numerical algorithms as well. We achieve this goal by conducting a thorough study on the first-order and second-order (sub)differentiation of real-valued functions in quaternion matrices, with a newly introduced operation called R-product as the key tool for our calculus. Combining with the classical optimization theory, we establish the first-order and the second-order optimality analysis for QMO. Particular treatments on convex functions, the ℓ 0 -norm and the rank function in quaternion matrices are tailored for a sparse low rank QMO model, arising from color image denoising, to establish its optimality conditions via stationarity. [ABSTRACT FROM AUTHOR]

Sylvester-type matrix equations have wide applications in system science, control theory, and so on. In this paper, we consider a constrained system of Sylvester-type matrix equations over the quaternions. We first derive the necessary and sufficient conditions for the system to have a solution and propose a formula of its general solution when it is solvable. As an application, we then investigate the η -Hermitian solution of a system. Moreover, we also give a numerical example to illustrate the main findings of this paper. [ABSTRACT FROM AUTHOR]

Purpose: Tyrosine kinase inhibitors (TKIs) targeting epidermal growth factor receptor (EGFR) improve the prognosis of lung adenocarcinoma (LUAD). However, the factors affecting its clinical efficacy remain unclear. This study aimed to determine the correlation between Osteopontin (OPN) and EGFR, and explore the inhibitory effect of first-generation TKI gefitinib on LUAD cells. Methods: The correlation between OPN and EGFR was determined through bioinformatics technology, and the clinical information as well as samples of related patients were collected to verify the relationship between them. Using three different NSCLC cell lines A549, H1299 and PC9, we studied the effects of OPN expression and EGFR phosphorylation on the first-generation TKI's efficacy in vitro. Results: Our data revealed that OPN staining positively linked to a more advanced clinical stage. Compared with the control group, LUAD cells with elevated OPN levels are more sensitive to the growth inhibitory effect of TKI. Knocking down of OPN decreased the response of cells to gefitinib. Besides, OPN also upregulated the phosphorylation of EGFR, thereby affecting the effect of TKI. Conclusion: OPN enhanced the sensitivity of LUAD cells to gefitinib by promoting EGFR phosphorylation. OPN may be a potential target for evaluating TKI efficacy and a potential target for molecular therapy. [ABSTRACT FROM AUTHOR]

In this paper, the authors derive the existence criteria and the formulae of the weighted Moore-Penrose inverse, the e-core inverse and the f-dual core inverse in rings. Also, new characterizations between weighted Moore-Penrose inverses and one-sided inverses along an element are given. [ABSTRACT FROM AUTHOR]

In this paper, we consider the generalized nonnegative tensor factorization (GNTF) problem, which arises in multiple-tissue gene expression and multi-target tracking. Based on the Karhsh-Kuhn-Tucker conditions, the necessary condition of the local solution for the GNTF problem is given. The proximal alternating nonnegative least squares method is designed to solve it, and its convergence theorem is also derived. Numerical examples show that the new method is feasible and effective. [ABSTRACT FROM AUTHOR]

In this note, we give some other generalizations of Hartfiel's inequality and the Brunn–Minkowski inequality to sector matrices, the results obtained improve those of Lin (Arch Math 104:93–100, 2015) and Liu (Linear Algebra Appl 508:206–213, 2016). [ABSTRACT FROM AUTHOR]

We first investigate some necessary and sufficient conditions for the solvability to a constraint system of coupled two-sided Sylvester-like quaternion tensor equations. We also construct an expression of the general solution to the system above when it is solvable. As an application of the system, we discuss some solvability conditions and the η -Hermitian solution to some system of Sylvester-like quaternion tensor equations. [ABSTRACT FROM AUTHOR]

We establish necessary and sufficient conditions for the existence of the reducible solution to the quaternion tensor equation A ∗ N X ∗ N B = C via Einstein product using Moore-Penrose inverse, and present an expression of the reducible solution to the equation when it is solvable. Moreover, to have a general solution, we give the solvability conditions for the quaternion tensor equation A 1 ∗ N X 1 ∗ M B 1 + A 1 ∗ N X 2 ∗ M B 2 + A 2 ∗ N X 3 ∗ M B 2 = C , which plays a key role in investigating the reducible solution to A ∗ N X ∗ N B = C . The expression of such a solution is also presented when the consistency conditions are met. In addition, we show a numerical example to illustrate this result. [ABSTRACT FROM AUTHOR]

This paper is concerned with solving the multilinear systems A x m - 1 = b whose coefficient tensors are mth-order and n-dimensional symmetric tensors. We first extend the accelerated overrelaxation (AOR) splitting method to solve the tensor equation. To improve the convergence, we develop a Newton-AOR (NAOR) method that hybridizes the Newton method and the accelerated overrelaxation scheme. Convergence analysis shows that the proposed methods converge under appropriate assumptions. Finally, some numerical examples are provided to show the effectiveness of the methods proposed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Arnoldi method of the right eigenvalue problem of the large-scale quaternion matrices. We use the real structure-preserving rather than the quaternion or the real structure, which has limitations in dealing with large quaternion matrices, to construct algorithms. The basic quaternion Arnoldi method is proposed to get the partial Schur decomposition of the quaternion matrices. Then, we give a novel algorithm for calculating the right eigenvectors of a quaternion Schur form. Furthermore, an explicitly restarted quaternion Arnoldi method (ERQAM) is presented to solve the right eigenpairs of the quaternion matrices. Finally, we provide five numerical examples which show the efficiency and accuracy of the proposed algorithms, and illustrate that the performance of ERQAM for large low rank quaternion matrices is better than that of the already known and brand-new methods. [ABSTRACT FROM AUTHOR]

It is desirable to evaluate the maximal violation of Bell inequalities as the violation of constraints indicates the quantum effect of correlation in composite quantum system. In this paper, we propose a new approach to compute the maximal violation of Bell inequalities for multipartite qubit via partially symmetric tensor. For a class of well known Bell inequalities, we find that their maximal violation values derived by partially symmetric tensors cover the previous results as a special case. This sheds new light on the applications of tensor in the quantum multipartite system. [ABSTRACT FROM AUTHOR]

We characterize linear transformations on matrices over commutative antinegative semirings that are monotone with respect to minus, star, and sharp partial orders. [ABSTRACT FROM AUTHOR]

Several inequalities are presented for sector matrices. First, an analogue of the AM-GM inequality is established. As applications of this inequality, similar inequalities are presented for singular values and norms. Finally, some unitarily invariant norm inequalities are obtained for sector matrices. [ABSTRACT FROM AUTHOR]

By keeping in mind the great number of applications of generalized Sylvester matrix equations in systems and control theory, in this paper we establish some necessary and sufficient conditions for the solvability to a system of eight generalized Sylvester matrix equations over the quaternion algebra. The general solution to this system is also constructed when it is solvable. Moreover, an algorithm and a numerical example are also given to make the results of this paper more practical in various fields of engineering. The findings of this paper generalize previous results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we discuss Hermitian solutions of split quaternion matrix equation $$AXB+CXD=E,$$ where X is an unknown split quaternion Hermitian matrix, and A, B, C, D, E are known split quaternion matrices with suitable size. The objective of this paper is to establish a necessary and sufficient condition for the existence of a solution and a solution formulas. Moreover, we provide numerical algorithms and numerical examples to exemplify the results. [ABSTRACT FROM AUTHOR]

In this paper, we first define a generalized ( f, g)-skew information $\left |I_{ \rho }^{(f, g)}\right |(A)$ and two related quantity $\left |J_{ \rho }^{(f, g)}\right |(A)$ and $\left |U_{ \rho }^{(f, g)}\right |(A)$ for any non-Hermitian Hilbert-Schmidt operator A and a density operator ρ on a Hilbert space H and discuss some properties of them. And then, we obtain the following uncertainty relation in terms of $\left |U_{ \rho }^{(f, g)}\right |(A)$ : which is a generalization of a known uncertainty relation in Ko and Yoo (J. Math. Anal. Appl. 383, 208-214, 11). [ABSTRACT FROM AUTHOR]

Super quantum discord based on weak measurements was introduced by Singh and Pati (Ann Phys 343:141-152, ). We propose a geometric way of quantifying quantum discord with weak measurements. It is shown that this geometric measure of quantum discord with weak measurements (GQDW) is linearly dependent on geometric measure of quantum discord (Dakic et al. in Phys Rev Lett 105:190502, ) and only captures partial quantumness of the states. It is found that the quantum correlation can be extracted by a sequence of infinitesimal weak measurements. Finally, the level surfaces of GQDW for Bell-diagonal states are depicted and the results are demonstrated by explicit example. [ABSTRACT FROM AUTHOR]

Cardiovascular diseases remain one of the major health problems worldwide. The worldwide research against cardiovascular diseases as well as genome wide association studies were successful in indentifying the loci associated with this prominent life-threatening disease but still a substantial amount of casualty remains unexplained. Over the last decade, the thorough understanding of molecular and biochemical mechanisms of cardiac disorders lead to the knowledge of various mechanisms of action of polyphenols to target inflammation during cardiac disorders. The present review article summarizes major mechanisms of polyphenols against cardiovascular diseases. [ABSTRACT FROM AUTHOR]

Wood plastic composite (WPC) of wood flour (WF), high density polyethylene (HDPE), maleic anhydride-grafted polyethylene (MAPE) and lubricant was prepared by extrusion, and then exposed to different temperatures to evaluate the effects of freezing and thermal treatment on its dimensional and mechanical properties. At elevated temperatures, WPC expanded rapidly initially, and then contracted slowly until reaching an equilibrium state. Treatment at 52°C and relative humidity of 50% for 16 days improved the mechanical properties of WPC: flexure, tensile strength, and izod unnotched impact strength increased by 8%, 10% and 15%, respectively. Wide-angle X-ray diffraction (XRD) tests showed that the degree of crystalization of HDPE in WPC declined with increasing treatment temperature. [ABSTRACT FROM AUTHOR]

Kevlar® fiber (KF) is a synthesized product with strong mechanical properties. We used KF as a reinforcement to improve the mechanical properties of wood-flour/polypropylene (WF/PP) composites. KF was pretreated with NaOH to improve its compatibility with the thermoplastic matrix. Maleated polypropylene (MAPP) was used as a coupling agent to improve the interfacial adhesion between KF, WF, and PP. Incorporation of KF improved the mechanical properties of WF/PP composites. Treatment of KF with NaOH resulted in further improvement in mechanical strength. Addition of 3% MAPP and 2% hydrolyzed KF (HKF) led to an increment of 93.8% in unnotched impact strength, 17.7% in notched impact strength, 86.8% in flexure strength, 50.8% in flexure modulus, and 94.1% in tensile strength compared to traditional WF/PP composites. Scanning electron microscopy of the cryo-fractured section of WF/PP showed that the HKF surface was rougher than the virgin KF, and the KF was randomly distributed in the composites, which might cause a mechanical interlocking between KF and polypropylene molecules in the composites. [ABSTRACT FROM AUTHOR]

Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f( X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX = B and YC = D respectively. As applications, we derive the necessary and sufficient conditions for the existence of maximal matrices of The corresponding expressions of the maximal matrices of H are presented when the existence conditions are met. In this case, we further prove the matrix function f( X,Y)is invariant under changing the pair ( X,Y). Moreover, we establish necessary and sufficient conditions for the system of matrix equations to have a Hermitian solution and the system of matrix equations to have a bisymmetric solution. The explicit expressions of such solutions to the systems mentioned above are also provided. In addition, we discuss the range of inertias of the matrix functions P ± QXQ* ± TYT* where X and Y are a nonnegative definite pair of solutions to some consistent matrix equations. The findings of this pape extend some known results in the literature. [ABSTRACT FROM AUTHOR]

The effect of maleic anhydride grafted styrene-ethylene- butylene-styrene block copolymer (SEBS-g-MAH) and in-situ grafting MAH on mechanical, dynamic mechanical properties of wood flour/recycled plastic blends composites was investigated. Recycled plastic polypropylene (PP), high-density polyethylene (HDPE) and polystyrene (PS), were mixed with wood flour in a high speed blender and then extruded by a twin/single screw tandem extruder system to form wood flour/recycled plastic blends composites. Results show that the impact properties of the composites were improved more significantly by using SEBS-g-MAH compatibilizer than by using the mixtures of MAH and DCP via reactive blending in situ. However, contrary results were observed on the tensile and flexural properties of the corresponding composites. In General, the mechanical properties of composites made from recycled plastic blends were inferior to those made from virgin plastic blends, especially in elongation break. The morphological study verified that the interfacial adhesion or the compatibility of plastic blends with wood flour was improved by adding SEBS-g-MAH or in-situ grafting MAH. A better interfacial bonding between PP, HDPE, PS and wood flour was obtained by in-situ grafting MAH than the addition of SEBS-g-MAH. In-situ grafting MAH can be considered as a potential way of increasing the interfacial compatibility between plastic blends and wood flour. The storage modulus and damping factor of composites were also characterized through dynamic mechanical analysis (DMA). [ABSTRACT FROM AUTHOR]

Rice-hull powder is widely used in manufacturing reinforced plastic composites. However, its weathering ability is rarely considered. We studied the performance of two types of rice-hull-polyethylene (RH-PE) composites after they were exposed outdoor to natural weathering for two years. The samples did not change in bending strength and elasticity modulus. At the end of the testing period, colour lightness had increased by more than 23% and total colour had changed by more than 9 units. This means the colour evidently differentiate from the original colour that the customers choose. The analyses of Fourier-transform infrared (FTIR) and X-ray photoelectron spectroscopy (XPS) showed that oxidation had occurred on sample surfaces. Red lumber presented an obvious C=O peak after weathering, while yellow lumber did not present an obvious peak as evidence of oxidation. Both types of lumbers showed a reduction of lignocellulosic groups and amorphous regions of PE. [ABSTRACT FROM AUTHOR]

For evaluation of the rheological and mechanical properties of highly filled wood plastic composites (WPCs), polypropylene/polyethylene (PP/PE) blends were grafted with maleic anhydride (MAH) to enhance the interfacial adhesion between wood fiber and matrix. WPCs were prepared from wood fiber up to 60 wt.% and modified PP/PE was blended by extrusion. The rheological properties were studied by using dynamic measurement. According to the strain sweep test, the linear viscoelastic region of composites in the melt was determined. The result showed that the storage modulus was independent of the strain at low strain region (<0.1%). The frequency sweep results indicated that all composites exhibited shear thinning behavior, and both the storage modulus and complex viscosity of MAH modified composites were decreased comparing to those unmodified. Flexural properties and impact strength of the prepared WPCs were measured according to the relevant standard specifications. The flexural and impact strength of the manufactured composites significantly increased and reached a maximum when MAH dosage was 1.0 wt.%, whereas the flexural modulus after an initial decreased, also increased with MAH dosage. The increase in mechanical properties indicated that the presence of anhydride groups enhanced the interfacial adhesion between wood fiber and PP/PE blends. [ABSTRACT FROM AUTHOR]

MA-SEBS as compatibilizer and impact modifier was incorporated into Polypropylene/Wood Fiber (PP/WF) to enhance interface adhesion and impact strength of the composite. The effect of MA-SEBS content on the impact fracture behavior of PP/WF composites was studied. The impact properties of composites with 8% MA-SEBS reached the maximum value. And further increasing of MA-SEBS content to 10% did not improve the fracture toughness, but improved the stiffness of composites by DMA analysis. This was attributed to the improved PP/WF adhesion. As the MA-SEBS content is more than 8%, the molecule interaction of PP and WF was expected to much stronger than lower MA-SEBS. Scanning electron microscopy (SEM) was performed to analyze the impact fracture surface and showed a stronger affinity for the wood surfaces. [ABSTRACT FROM AUTHOR]

The chemical components of dichloromethane extractives for Sawara Falsecypress heartwood were analyzed with GC/MS except for basic chemical composition analysis for heartwood with Chinese standard method. 14 kinds of compounds were identified according to the computer compounds library data. The major compounds in dichloromethane extractives comprised of terpene and naphthalene derivatives. The experiments of antifungal effects of the dichloromethane extractive on Aspergillus niger were also carried out. The result showed that the dichloromethane extractive from Sawara Falsecypress has no or weak antifungal capability. [ABSTRACT FROM AUTHOR]

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 $$\mathop {\min }\limits_{X \in \phi } $$ | X − E|F was given, where E is a given complex matrix and ϕ 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. [ABSTRACT FROM AUTHOR]

In this paper, the maximal and minimal ranks of the solution to a system of matrix equations over H, the real quaternion algebra, were derived. A previous known result could be regarded as a special case of the new result. [ABSTRACT FROM AUTHOR]

A study was conducted to investigate the effects of compatibilizers, including Maleic anhydride grafted polypropylene (MA-PP) and maleic anhydride grafted ethylene-propylene-diene copolymer (MA-EPDM), on wood-flour/polypropylene (WF/PP) composites. WF/PP composites were prepared by direct extrusion profiles using a twin-screw/single-screw extruder system. DMA analysis showed that the loss factor of composites decreased and the storage modulus improved in the presence of MA-PP, which indicated much better interfacial adhesion between the PP matrix and wood flour filler than in the absence of compatibilizer. Morphological feature based on SEM observation showed that MA-PP and MA-EPDM improved the dispersion of the wood particles in the plastic matrix. MA-EPDM is a soft segment, although it improved the interfacial adhesion, storage modulus decreases with adding of MA-EPDM. As compatibilizer of wood-flour/polypropylene composites, both DMA analysis and SEM feature proved that MA-PP was superior to MA-EPDM. [ABSTRACT FROM AUTHOR]

In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In addition, a criterion for a matrix to be generalized bipositive semidefinite was determined. [ABSTRACT FROM AUTHOR]

The quantification of coherence is central in quantum information theory and far from being fully understood, particularly for multipartite quantum states. In this work, we first propose the coherence eigenvalue for multipartite pure quantum states and then define the coherence measure for a given multipartite pure or mixed state based on it. It is found that the convex roof coherence measure is equal to the geometric measure based on fidelity. This finding allows us to give an alternative way to prove that the geometric measure of coherence is monotone under selective measurements on average. The other two new coherence measures based on coherence eigenvalue are presented, and their properties are also investigated. As an application, the bounds of several well-known coherence measures are derived by using of coherence eigenvalue. In particular, by proposing a new coherence witness which is related to coherence eigenvalue, we obtain a bound to robustness of coherence and give it a corresponding geometric interpretation. [ABSTRACT FROM AUTHOR]

We show that, given a single-qubit state, the maximal possible value of disturbance induced by unitary evolution with respect to time coincides with the b o n a f i d e coherence measure based on skew information up to a constant. This establishes the exact relation between the impact power of Hamiltonian and the coherence measure subject to the eigenbasis of Hamiltonian. We present closed formula of impact power of Hamiltonian, thus equivalently giving an evaluation of coherence measure for any generic basis. In particular, for 2 × N quantum system, we prove that the impact power of local Hamiltonian is equal to the partial coherence based on skew information. By employing the special form of the corresponding unitary operator, we derive the lower and upper bounds of impact power for any Hamiltonian, which in turn provides the allowed amount of coherence for arbitrary generic basis. Finally, for two-qubit pure state, we demonstrate that there is an interesting connection between partial coherence and CHSH inequality. [ABSTRACT FROM AUTHOR]