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The biconjugate gradients (BiCG) and biconjugate residual (BiCR) methods are attractive ways for solving nonsymmetric linear system A x = b. In this paper, the BiCG and BiCR methods are extended to solve the high order Stein tensor equation. The convergent properties of the developed iterative algorithms are studied. Numerical examples are provided to confirm the theoretical results, which demonstrate that the proposed algorithms are effective and feasible for solving the Stein tensor equation. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the solvability of a system of constrained two-sided coupled generalized Sylvester quaternion matrix equations. Some necessary and sufficient conditions for the existence of solutions to this system are derived in terms of the ranks and the generalized inverses of the coefficient matrices. Moreover, we find an expression of the general solution to this system when the solvability conditions are satisfied. Finally, a numerical example is presented to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Cramer’s rule for the general solution to the system of quaternion matrix equations A 1 X B 1 = C 1 , A 2 X B 2 = C 2 , and Cramer’s rule for the general solution to the generalized Sylvester quaternion matrix equation A X B + C Y D = E , respectively. As applications, we derive the determinantal expressions for the Hermitian solutions to some quaternion matrix equations. The findings of this paper extend some known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we establish some necessary and sufficient solvability conditions for a system of quaternary coupled Sylvester-type real quaternion matrix equations in terms of ranks and generalized inverses of matrices. An expression of the general solution to this system is given when it is solvable. Also, a numerical example is presented to illustrate the main result of this paper. The findings of this paper widely generalize the known results in the literature. The main results are also valid over the real number field and the complex number field. [ABSTRACT FROM AUTHOR]

Let R and H m × n stand, respectively, for the real number field and the set of all m × n matrices over the real quaternion algebra H = { a 0 + a 1 i + a 2 j + a 3 k | i 2 = j 2 = k 2 = ijk = − 1 , a 0 , a 1 , a 2 , a 3 ∈ R } . For η ∈ { i, j, k }, a real quaternion matrix A ∈ H n × n is said to be η -Hermitian if A η * = A where A η * = − η A * η , and A * stands for the conjugate transpose of A , arising in widely linear modeling. We present a simultaneous decomposition for a set of nine real quaternion matrices involving η -Hermicity with compatible sizes: A i ∈ H p i × t i , B i ∈ H p i × t i + 1 , and C i ∈ H p i × p i , where C i are η -Hermitian matrices, ( i = 1 , 2 , 3 ) . As applications of the simultaneous decomposition, we give necessary and sufficient conditions for the existence of an η -Hermitian solution to the system of coupled real quaternion matrix equations A i X i A i η * + B i X i + 1 B i η * = C i , ( i = 1 , 2 , 3 ) , and provide an expression of the general η -Hermitian solutions to this system. Moreover, we derive the rank bounds of the general η -Hermitian solutions to the above-mentioned system using ranks of the given matrices A i , B i , and C i as well as the block matrices formed by them. Finally some numerical examples are given to illustrate the results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, some necessary and sufficient conditions are established for the constraint generalized Sylvester matrix equations to have a common solution. The expression of the general common solution is also given under the solvable conditions. In addition, a numerical example is presented to illustrate the presented theory. [ABSTRACT FROM AUTHOR]

In this paper, we give some necessary and sufficient conditions for the consistence of the system of quaternion matrix equations A 1 X = C 1 , Y B 1 = D 1 , A 2 W = C 2 , Z B 2 = D 2 , A 3 V = C 3 , V B 3 = C 4 , A 4 V B 4 = C 5 , A 5 X + Y B 5 + C 6 W + Z D 6 + E 6 V F 6 = G 6 , and constitute an expression of the general solution to the system when it is solvable. The outcomes of this paper encompass some recognized results in the collected works. In addition, we establish an algorithm and a numerical example to illustrate the theory constructed in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonlinear matrix equations X + A * X q A = Q ( 0 < q ≤ 1 ) and X − A * X q A = Q ( q > 1 ) . Necessary and sufficient conditions for the (unique) existence of Hermitian positive definite solutions of these equations are derived. Effective iterative algorithms are also provided to obtain the unique solution of X + A * X q A = Q ( 0 < q ≤ 1 ) and the minimal and maximal Hermitian positive definite solutions of X − A * X q A = Q ( q > 1 ) . Numerical examples are included to illustrate the efficiency of the presented iteration algorithms. [ABSTRACT FROM AUTHOR]

Let H m × n be the set of all m × n matrices over the real quaternion algebra H = { c 0 + c 1 i + c 2 j + c 3 k ∣ i 2 = j 2 = k 2 = i j k = − 1 , c 0 , c 1 , c 2 , c 3 ∈ R } . A ∈ H n × n is known to be η -Hermitian if A = A η * = − η A * η , η ∈ { i , j , k } and A * means the conjugate transpose of A . We mention some necessary and sufficient conditions for the existence of the solution to the system of real quaternion matrix equations including η -Hermicity A 1 X = C 1 , A 2 Y = C 2 , Y B 2 = D 2 , Y = Y η * , A 3 Z = C 3 , Z B 3 = D 3 , Z = Z η * , A 4 X + ( A 4 X ) η * + B 4 Y B 4 η * + C 4 Z C 4 η * = D 4 , and also construct the general solution to the system when it is consistent. The outcome of this paper diversifies some particular results in the literature. Furthermore, we constitute an algorithm and a numerical example to comprehend the approach established in this treatise. [ABSTRACT FROM AUTHOR]

In this paper, we define and discuss the Moore–Penrose inverses of matrices with quaternion polynomial entries. When the Moore–Penrose inverses exist, we prove that Leverrier–Faddeev algorithm works for these matrices by using generalized characteristic polynomials. Furthermore, after studying interpolations for quaternion polynomials, we give an efficient algorithm to compute the Moore–Penrose inverses. We developed a Maple package for quaternion polynomial matrices. All algorithms in this paper are implemented, and tested on examples. [ABSTRACT FROM AUTHOR]

This paper studies some systems of coupled generalized Sylvester matrix equations. We present some necessary and sufficient conditions for the solvability to these systems. We give the expressions of the general solutions to the systems when their solvability conditions are satisfied. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the linear parameterized inverse eigenvalue problem of bisymmetric matrices which is described as follows: We first establish the structure of bisymmetric matrices. Based on the Newton-type iterative method, we then turn Problem I into the inverse eigenvalue problems of symmetric matrices with small sizes, and solve these problems. Finally, we present numerical examples to illustrate our results. [Copyright &y& Elsevier]

Abstract: By using the complex representation of quaternion matrices, and the Moore–Penrose generalized inverse, we derive the expressions of the least squares solution with the least norm, the least squares pure imaginary solution with the least norm, and the least squares real solution with the least norm for the quaternion matrix equation , respectively. Finally, we discuss their applications in color image restoration. [Copyright &y& Elsevier]

Abstract: In this paper, we give some necessary and sufficient solvability conditions for the mixed Sylvester matrix equations, and parameterize general solution when it is solvable. Moreover, we investigate the maximal and minimal ranks of the general solution, and maximal and minimal ranks and inertias of Hermitian part of solution, respectively. [Copyright &y& Elsevier]

Abstract: In this paper, the solvability conditions and the explicit expressions of the generalized bisymmetric and bi-skew-symmetric solutions of the matrix equation are respectively established by applying two methods. Then the maximal and minimal ranks of the solutions are derived. If the solvability conditions are not satisfied, the generalized bisymmetric and bi-skew-symmetric least squares solutions of the matrix equation are considered, and the generalized bisymmetric and bi-skew-symmetric least squares solutions with the minimum norm are also obtained. In addition, two algorithms are provided to compute the generalized bi (skew-) symmetric least squares solution, and some examples are given to illustrate that the algorithms are feasible. [Copyright &y& Elsevier]

Abstract: Consider the Hermitian matrix function subject to a consistent system of matrix equations where means conjugate transpose. In this paper we first establish explicit expansion formulas to calculate the global maximal and minimal ranks and inertias of the Hermitian matrix function , then we use the derived formulas to give necessary and sufficient conditions for system (0.1) to have Re-nonnegative definite, Re-nonpositive definite, Re-positive definite, and Re-negative definite solutions. Moreover, as another application of the derived formulas, we establish necessary and sufficient conditions for the solvability to the system of matrix equations and provide an expression of the general solution to (0.2) when it is solvable. The findings of this paper widely extend the known results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we derive an alternative more condensed Cramer rule for the unique solution of some restricted left and right systems of quaternion linear equations. The findings of this paper extend some known results in the literature. [Copyright &y& Elsevier]

Abstract: We in this paper consider the bisymmetric nonnegative definite solution with extremal ranks and inertias to a system of quaternion matrix equations AX = C, XB = D. We derive the extremal ranks and inertias of the common bisymmetric nonnegative definite solution to the system. The general expressions of the bisymmetric nonnegative definite solution with extremal ranks and inertias to the system mentioned above are also presented. In addition, we give a numerical example to illustrate the results of this paper. [Copyright &y& Elsevier]

Abstract: Let denote the set of all m × n matrices over the quaternion algebra and be involutions. We say that is (P, Q)-symmetric (or (P, Q)-skewsymmetric) if A = PAQ (or A =− PAQ). We in this paper mainly investigate the (P, Q)-(skew)symmetric maximal and minimal rank solutions to the system of quaternion matrix equations AX = B, XC = D. We present necessary and sufficient conditions for the existence of the maximal and minimal rank solutions with (P, Q)-symmetry and (P, Q)-skewsymmetry to the system. The expressions of such solutions to this system are also given when the solvability conditions are satisfied. A numerical example is presented to illustrate our results. The findings of this paper extend some known results in this literature. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the determinantal representations of the generalized inverses , and over the quaternion skew field by the theory of the column and row determinants. In addition, we derive some generalized Cramer rules for the unique solution of some restricted quaternion matrix equations. The findings of this paper extend some known results in the literature. [Copyright &y& Elsevier]

Abstract: We present necessary and sufficient conditions for the existence of a positive solution to the system of adjointable operator equations over Hilbert -modules. We also derive a representation for a general positive solution to this system when the solvability conditions are satisfied. The results of this paper extend some known results in the literature. [ABSTRACT FROM AUTHOR]

Abstract: Suppose that p(X, Y)= A − BX − X (∗) B (∗) − CYC (∗) and q(X, Y)= A − BX + X (∗) B (∗) − CYC (∗) are quaternion matrix expressions, where A is persymmetric or perskew-symmetric. We in this paper derive the minimal rank formula of p(X, Y) with respect to pair of matrices X and Y = Y (∗), and the minimal rank formula of q(X, Y) with respect to pair of matrices X and Y =−Y (∗). As applications, we establish some necessary and sufficient conditions for the existence of the general (persymmetric or perskew-symmetric) solutions to some well-known linear quaternion matrix equations. The expressions are also given for the corresponding general solutions of the matrix equations when the solvability conditions are satisfied. At the same time, some useful consequences are also developed. [ABSTRACT FROM AUTHOR]

Abstract: Let R and S be m × m and n × n nontrivial real symmetric involutions. An m × n complex matrix A is termed (R, S)-conjugate if , where denotes the conjugate of A. In this paper, necessary and sufficient conditions are established for the existence of the (R, S)-conjugate solution to the system of matrix equations AX = C and XB = D. The expression is also presented for such solution to this system. In addition, the explicit expression of this solution to the corresponding optimal approximation problem is obtained. Furthermore, the least squares (R, S)-conjugate solution with least norm to this system mentioned above is considered. The representation of such solution is also derived. Finally an algorithm and numerical examples are given. [ABSTRACT FROM AUTHOR]

Abstract: We establish necessary and sufficient conditions for the existence of the general common Hermitian solution to the equations for adjointable operators between Hilbert -modules, and present an expression for the common Hermitian solution to the equations in terms of Moore–Penrose inverse of operators when the solvability conditions are satisfied. The findings of this paper extend some known results in the literature. [Copyright &y& Elsevier]

Abstract: Acid-catalyzed 1-octene reactions with phenol and mixtures of phenol with water, acetic acid and 1-butanol were studied as partial bio-oil upgrading models. Bio-oil from fast biomass pyrolysis has poor fuel properties due to the presence of substantial amounts of water, carboxylic acid, phenolic derivatives and other hydroxyl-containing compounds. Additions across olefins offer a route to simultaneously lower water content and acidity while increasing hydrophobicity, stability and heating value. Amberlyst15, Dowex50WX2 and Dowex50WX4 effectively catalyzed phenol O- and C-alkylation from 65 to 120°C, giving high O-alkylation selectivities in the presence of water, acetic acid and 1-butanol. Octanols and dioctyl ethers were formed from water and octyl acetates and phenol acetates from acetic acid. Phenol alkylation slowed in the presence of water. Dowex50WX2 and Dowex50WX4 were more stable in the presence of water than Amberlyst15 and were successfully recycled. Adding 1-butanol to phenol/water/1-octene, gave emulsion-like mixtures which improved phenol conversion and olefin hydration. [Copyright &y& Elsevier]

Abstract: Let be the real quaternion algebra and denote the set of all matrices over . Let and be involutions, i.e., . A matrix is said to be -symmetric if . This paper studies the system of linear real quaternion matrix equationsWe present some necessary and sufficient conditions for the existence of a solution to this system and give an expression of the general solution to the system when the solvability conditions are satisfied. As applications, we discuss the necessary and sufficient conditions for the systemto have a -symmetric solution. We also show an expression of the -symmetric solution to the system when the solvability conditions are met. Moreover, we provide an algorithm and a numerical example to illustrate our results. The findings of this paper extend some known results in the literature. [Copyright &y& Elsevier]

Abstract: We in this paper first establish a new expression of the general solution to the consistent system of linear quaternion matrix equations , , , which was investigated recently [Q.W. Wang, H.X. Chang, C.Y. Lin, P-(skew)symmetric common solutions to a pair of quaternion matrix equations, Appl. Math. Comput. 195 (2008) 721–732], then derive the maximal and minimal ranks and the least-norm of the general solution to the system mentioned above. Some previous known results can be viewed as special cases of the results of this paper. [Copyright &y& Elsevier]

• We in this paper propose the bi-conjugate gradient and bi-conjugate residual methods in their tensor forms for solving the Sylvester tensor equation. • BiCG-BTF and BiCR-BTF methods are superior to the modified conjugate gradient method in terms of both the number of iteration steps and CPU time. • From the nearest Kronecker product, the convergence rate of the preconditioned BiCG-BTF and BiCR-BTF methods is about twice that of the PGMRES-BTF method. This paper is concerned with solving high order Sylvester tensor equation arising in control theory. We propose the tensor forms of the bi-conjugate gradient and bi-conjugate residual methods for solving the tensor equation. To improve their performance, two preconditioned iterative algorithms based on the nearest Kronecker product are developed for finding its solution. We also prove that the proposed algorithms are convergent to an exact solution within finite iteration steps for any initial tensor in the absence of round-off errors. At last, some numerical examples are provided to illustrate the feasibility and validity of the algorithms proposed. [ABSTRACT FROM AUTHOR]

Abstract: A variety of rank formulas of some matrix expressions and certain partitioned matrices with respect to the generalized inverse are established. Some necessary and sufficient conditions are given by using the rank formulas presented in this paper for two, three and four ordered matrices to be independent in the generalized inverse . As special cases, necessary and sufficient conditions are derived for two, three and four ordered matrices to be independent in the weighted Moore–Penrose inverse and the Drazin inverse. Some known results can be regarded as the special cases of the results in this paper. [Copyright &y& Elsevier]

Abstract: We in this paper establish necessary and sufficient conditions for the existence of and an explicit expression for a common solution to six classical linear quaternion matrix equations A 1 X = C 1, XB 1 = C 2, A 2 X = C 3, XB 2 = C 4, A 3 XB 3 = C 5, and A 4 XB 4 = C 6. As applications, symmetric, persymmetric and centrosymmetric solutions to certain systems of quaternion matrix equations are presented. Furthermore, we give an example to illustrate the result of this paper. Some known results can be regarded as the special cases of this paper. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the formulas of the maximal and minimal ranks of the quaternion matrix expression where X is a variant quaternion matrix subject to quaternion matrix equations . As applications, we give a new necessary and sufficient condition for the existence of solutions to the system of matrix equations , which was investigated by Wang [Q.W. Wang, A system of four matrix equations over von Neumann regular rings and its applications, Acta Math. Sin., 21(2) (2005) 323–334], by rank equalities. In addition, extremal ranks of the generalized Schur complement with respect to an inner inverse A − of A, which is a common solution to quaternion matrix equations , are also considered. Some previous known results can be viewed as special cases of the results of this paper. [Copyright &y& Elsevier]

Abstract: An n × n quaternion matrix A is termed P-symmetric (or P-skewsymmetric) if A = PAP (or A =−PAP), where P is an n × n nontrivial quaternion involution. In this paper, we first establish necessary and sufficient conditions for the existence and the expression of the general solution to the system of quaternion matrix equations , then use the results on the system mentioned above to give necessary and sufficient conditions for the existence and the representations of P-symmetric and P-skewsymmetric solutions to the system of quaternion matrix equations A a X = C a and A b XB b = C b . Furthermore, we establish representations of P-symmetric and P-skewsymmetric quaternion matrices. A numerical example is presented to illustrate the results of this paper. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the maximal and minimal ranks of the solution to the consistent system of quaternion matrix equations and , which was investigated recently by Wang [Q.W. Wang, The general solution to a system of real quaternion matrix equations, Comput. Math. Appl. 49 (2005) 665–675]. Moreover, corresponding results on some special cases are presented. As an application, a necessary and sufficient condition for the invariance of the rank of the general solution to the system mentioned above is presented. Some previous known results can be regarded as the special cases of this paper. [Copyright &y& Elsevier]

Abstract: Assume that the linear quaternion matrix expression f(X 1, X 2)= A − A 3 X 1 B 3 − A 4 X 2 B 4 where X 1, X 2 are variant quaternion matrices. In this paper, we derive the maximal and minimal ranks of f(X 1, X 2) subject to consistent systems of quaternion matrix equations A 1 X 1 = C 1, X 1 B 1 = C 2 and A 2 X 2 = C 3, X 2 B 2 = C 4. Moreover, corresponding results on some special cases are presented. As applications, we give necessary and sufficient conditions for the existence of solutions to some systems of quaternion matrix equations. Some previous known results can be regarded as the special cases of this paper. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the system of matrix equations, A 1 X = C 1, A 2 X = C 2, A 3 XB 3 = C 3, and A 4 XB 4 = C 4, over the real quaternion algebra . A necessary and sufficient condition for the existence and the expression of the general solution to the system are given. As particular cases, the corresponding results on other systems over are also obtained. [Copyright &y& Elsevier]

Abstract: In this paper we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra . Necessary and sufficient conditions are obtained for the matrix equation AX = C and the following systems to have bisymmetric solutions, and the system to have centrosymmetric solutions. The expressions of such solutions of the matrix and the systems mentioned above are also given. Moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over are also mentioned. [Copyright &y& Elsevier]

In this paper we consider the classical system of matrix equationsA1XB1=C1,A2XB2=C2over R, an arbitrary regular ring with identity. Necessary and sufficient conditions for the existence and the expression of the general solution to the system are derived. As an application, the linear matrix equation AXB+CYD=E over R is considered. [Copyright &y& Elsevier]

Let Ω be a finite dimensional central algebra with an involutorial antiautomorphism σ and char Ω≠2, Ωn×n be the set of all n×n matrices over Ω. A=(aij)∈Ωn×n is called bisymmetric if aij=an−i+1,n−j+1=σ(aji) and biskewsymmetric if aij=−an−i+1,n−j+1=−σ(aji). The following systems of generalized Sylvester equations over Ω[λ]:A1X−YB1=C1,(I)&z.tdfnc;AsX−YBs=Cs,A1XB1−C1XD1=E1,(II)&z.tdfnc;AsXBs−CsXDs=Es,are considered. Necessary and sufficient conditions are given for the existence of constant solutions with bi(skew)symmetric constrains to (I) and (II). As a particular case, auxiliary results dealing with the system of Sylvester equations are also presented. [Copyright &y& Elsevier]

Aim : To investigate the association of osteoproterin (OPG) gene polymorphisms 163A/G (rs3102735), 245T/G (rs3134069) with susceptibility to rheumatoid arthritis (RA) in Chinese Han population. Objective : To study the correlation between the disease of rheumatoid arthritis (RA) in Chinese Han group and the association of osteoproterin (OPG) gene polymorphisms 163A/G(rs3102735) and 245T/G (rs3134069). Approaches : 205 RA patients and 171 healthy control subjects were participated into this study. Genotype analysis was conducted by polymerase chain reaction-based restriction fragment length polymorphism and was subsequently confirmed by DNA sequencing. Odd ration (OR) and 95% confidence intervals (95% CI) were calculated for the risk of genotype and allele. Consequences : OPG gene polymorphisms 163A/G, 245T/G conformed to the Hardy–Weinberg equilibrium. The statistical differences in genotype of AA, AG, GG at 163A/G locus were founded in RA and controls. The G allele was associated with an increased risk of RA, with OR 1.219 (95% CI: 1.066–2.339). According to the observation, there are no significant differences between the RA and control groups with respect to genotype and allele frequencies of OPG gene 245T/G ( χ 2 = 0.734, 0.518, p > 0.05). Conclusion : The OPG gene 163A/G SNP may be associated with the susceptibility of RA, G allele may be the risk factor for the development of RA. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider matrices with entries from a semiring S. We first discuss some generalized inverses of rectangular and square matrices. We establish necessary and sufficient conditions for the existence of the Moore–Penrose inverse of a regular matrix. For an matrix A, an matrix P and a square matrix Q of order m, we present necessary and sufficient conditions for the existence of the group inverse of QAP with the additional property that is a inverse of A. The matrix product used here is the usual matrix multiplication. The result provides a method for generating elements in the set of inverses of an matrix A starting from an initial {1} inverse of A. We also establish a criterion for the existence of the group inverse of a regular square matrix. We then consider a semiring structure made up of matrices with the addition defined entry-wise and the multiplication defined as in the case of the Hadamard product of complex matrices. In the semiring , we present criteria for the existence of the Drazin inverse and the Moore–Penrose inverse of an matrix. When S is commutative, we show that the Hadamard product preserves the Hermitian property, and provide a Schur-type product theorem for the product of a positive semidefinite matrix A and an matrix C. [Copyright &y& Elsevier]

Abstract: We establish necessary and sufficient conditions for the existence of a Hermitian solution to the system of equations for adjointable operators between Hilbert C ∗-modules, and provide an expression for the general Hermitian solution to the system. We present necessary and sufficient conditions for the existence of a unique Hermitian solution to the systems and of adjointable operators between Hilbert C ∗-modules. Several examples are given to explain the use of the theory. Some of the findings of this paper extend some known results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, based upon the phenomenon that melamine can obviously enhance the CL signal of the luminol–H2O2 system in basic medium, a simple, rapid and sensitive flow injection chemiluminescence (FI-CL) method for the determination of melamine has been developed. Under the optimum conditions, the linear range for the determination of melamine was 0.2–80μgmL−1 with a detection limit of 0.12μgmL−1 calculated as proposed by IUPAC and a relative standard deviation of 3.26% for 11 solutions of 10μgmL−1 melamine on the same day. The proposed method was satisfactorily applied to determine melamine in milk-based products and satisfactory results were obtained without interferences from the sample matrix. Moreover, one assay produce takes only 25s and the minimum sampling rate is about 120 samplesh−1, which indicated that the FI-CL method was suitable for high throughput and real-time melamine analysis. [Copyright &y& Elsevier]

Abstract: Upgrading bio-oil by addition reactions across olefins represents a route to refine bio-oil to combustible and stable oxygen-containing fuels. Development and application of highly active strong solid acid catalysts with good hydrothermal stability has become a key determinant for success, because bio-oil’s complexity includes large amounts of water. Temperatures of 120°C or more are needed for satisfactory kinetics. Batch upgrading of a model bio-oil (phenol/water/acetic acid/acetaldehyde/hydroxyacetone/d-glucose/2-hydroxymethylfuran) over five water-tolerant solid acid catalysts (Dowex50WX2, Amberlyst15, Amberlyst36, silica sulfuric acid (SSA) and Cs2.5H0.5PW12O40 supported on K-10 clay (Cs2.5/K-10, 30wt.%)) with 1-octene/1-butanol were studied at 120°C/3h. SSA, ▪, exhibited the highest water tolerance and activity. Upgrading using olefin/1-butanol is complex, involving many simultaneous competing esterification, etherification, olefin hydration, phenol alkylation, aldol condensation, sugar dehydration etc. reactions. [Copyright &y& Elsevier]