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Mesenchymal stem cells (MSCs) can be obtained from a variety of human tissues. Placenta has become an attractive stem cell source for potential applications in regenerative medicine and tissue engineering. The aim of this study was to localize and characterize MSCs within human chorionic membranes (hCMSCs). For this purpose, immunofluorescence labeling with CD105 and CD90 were used to determine the distribution of MSCs in chorionic membranes tissue. A medium supplemented with a synthetic serum and various concentrations of neurotrophic factors and cytokines was used to induce hCMSCs to neural cells. The results showed that the CD90 positive cells were scattered in the chorionic membranes tissue, and the CD105 positive cells were mostly located around the small blood vessels. hCMSCs expressed typical mesenchymal markers (CD73, CD90, CD105, CD44 and CD166) but not hematopoietic markers (CD45, CD34) and HLA-DR. hCMSCs differentiated into adipocytes, osteocytes, chondrocytes, and neuronal cells, as revealed by morphological changes, cell staining, immunofluorescence analyses, and RT-PCR showing the tissue-specific gene presence for differentiated cell lineages after the treatment with induce medium. Human chorionic membranes may be the source of MSCs for treatment of nervous system injury.

Background To establish a novel method based on time-resolved immunofluorometric assay (TR-IFMA) with higher sensitivity and a broader detection range for detecting serum hepatitis B virus large surface protein (L protein). Methods The precision, sensitivity, specificity, coefficient of recovery, and stability of the assay were evaluated and comparison with the classical enzyme-linked immunosorbent assay (ELISA) was also executed. Results The precision, specificity, and sensitivity of the TR-IFMA were clearly better than ELISA. Particularly, the sensitivity was 0.1 ng/ml; moreover, the specificity was 100%, 96%, 92.5%, 96.9%, 97.8%, and 100% in the sera of healthy blood donors, systemic lupus erythematosus (SLE) patients, rheumatoid arthritis (RA) patients, hepatitis C virus (HCV) patients, cytomegalovirus (CMV) infection patients, and pregnant patients, respectively. Meanwhile, we observed that the established TR-IFMA kit has a wider acceptable linear range of 0.63–10,367 ng/ml rather than the regular commercial ELISA kit having range of only 10.12–1095.9 ng/ml. Subsequently, correlation coefficient between the TR-IFMA and ELISA was 0.8009. The intra- and interassay precision rates were less than 5% for three different concentrations. The average recovery rate for L protein was 101.17%. In sum, the established assay kit performed better in terms of stability than the commercial ELISA kit. Conclusion The TR-IFMA that we developed for L protein presented a higher sensitivity and wider detecting range than regular commercial ELISA. Therefore, this TR-IFMA has promising value both in the screening of HBV and monitoring of antiviral therapy.

In this paper, we present the explicit expression for the group inverse of the sum of two matrices. As an application, the explicit expression for the group inverse of the anti-triangular block matrix $\begin{pmatrix}A&B\\C&0\end{pmatrix}$ and $\begin{pmatrix}0&B\\C&D\end{pmatrix}$ are obtained without any conditions on sub-blocks

Let and be Banach spaces, and let be a bounded linear operator. In this paper, we first define and characterize the quasi-linear operator (resp., out) generalized inverse (resp., ) for the operator , where and are homogeneous subsets. Then, we further investigate the perturbation problems of the generalized inverses and . The results obtained in this paper extend some well-known results for linear operator generalized inverses with prescribed range and kernel.

Let $\R $ be a ring with unit 1 and $a\in \R, \bar{a}=a+��a\in \R $ such that $a^#$ exists. In this paper, we mainly investigate the perturbation of the group inverse $a^#$ on $\R$. Under the stable perturbation, we obtain the explicit expressions of $\bar{a}^#$. The results extend the main results in Xue (2007), and Xue and Chen (2007) and some related results in Xue (2012). As an application, we give the representation of the group inverse of the matrix d&b c&0 on the ring $\R$ for certain $d, b, c\in\R$., 10 pages, Filomat (accepted)

In this paper, we investigate the various different generalized inverses in a Banach algebra with respect to prescribed two idempotents $p$ and $q$. Some new characterizations and explicit representations for these generalized inverses, such as $a^{(2)}_{p,q}$, $a^{(1,2)}_{p,q}$ and $a^{(2,l)}_{p,q}$ will be presented. The obtained results extend and generalize some well--known results for matrices or operators., 17 pages

The mass concentration and major chemical components of fine particulate matter were measured before, during and after Beijing's massive parade commemorating 70th anniversary of the Chinese Victory in World War II on September 3, 2015. Regional emission inventory, positive matrix factorization (PMF), observations from space and backward air mass trajectories were jointly applied to identify the major pollution sources and their temporal and spatial variations. The contributions of emissions variations and the meteorological conditions related to the “parade blue” phenomenon in Beijing and its surrounding areas were investigated in detail. The main cause of the decreased PM 2.5 mass concentration was attributed to the absolute reduction in emissions of primary air pollutants. The chemical composition of PM 2.5 varied significantly before, during and after the parade. Fugitive dust particles were well controlled, the secondary formation of PM 2.5 was reduced along with the controlled gaseous precursors' emissions from vehicles and industrial sources during the temporary intensified control period. During the parade period, the SO 2 and NO 2 column concentrations in Beijing and the surrounding areas decreased sharply, indicating that the coordinated reduction in primary emissions from the surrounding areas of Beijing played an important role in lowering the ambient concentration of SO 2 and NO 2 and accordingly lowered PM 2.5 and improved the regional air quality. A comparison of the temperature, humidity, and wind speed and direction during the same periods in 2014 and 2015 showed that the meteorological conditions positively influenced the achievement of “parade blue”.

Let $\A$ and $\B$ be unital Banach algebras and $\phi\colon\A\to\B$ be a unital continuous homomorphism. We prove that if $\phi$ is relatively spectral (i.e., there is a dense subalgebra $X$ of $\A$ such that $\sp_\B(\phi(a))=\sp_\A(a)$ for every $a\in X$) and has dense range, then $\phi$ induces monomorphisms from $K_i(\A)$ to $K_i(\B)$, $i=0,1$., Comment: 6 pages

In this article, we give the density functions of the singular quaternion normal matrix and the singular quaternion Wishart matrix. Furthermore, we also give the density functions of certain singular quaternion β-matrix and the singular quaternion F-matrix in terms of the density function of the singular quaternion Wishart matrix and hypergeometric functions of quaternion matrix argument.

Let M be a separable compact Hausdorff space with dim M ? 2 and ? : M ? M be a homeomorphism with prime period p (p ? 2). Set M? = {x ( M|?(x) = x} = ( and M0 = M\M? . Suppose that M0 is dense in M and H2(M0/?, Z) ( 0, H2(?(M0/?), Z) ( 0. Let M' be another separable compact Hausdorff space with dim M' ? 2 and ?' be the self-homeomorphism of M' with prime period p. Suppose that M'0 = M'\M'?' is dense in M'. Then C(M) ? ?Zp ( C(M') ? ?'Zp if there is a homeomorphism F from M/? onto M'/?' such that F(M?) = M'?'. Thus, if (M, ?) and (M', ?') are orbit equivalent, then C(M) ? ?Zp ( C(M') ? ?'Zp. 2010 Mathematics Subject Classifications. 46L05. .

We define zonal polynomials of quaternion matrix argument and deduce some important formulae of zonal polynomials and hypergeometric functions of quaternion matrix argument. As an application, we give the distributions of the largest and smallest eigenvalues of a quaternion central Wishart matrix $W\sim\mathbb{Q}W(n,\Sigma)$, respectively., Comment: 22 pages. Communications in Statistics - Theory and Methods (appear)

Let A and B be unital Banach algebras and T : A ? B be a unital continuous homomorphism. Put J = Ker T. Let FredT (A) = {x ? A|T (x) is invertible in B} and Fred0T(A) = {x + k|x is invertible in A, k ? J}. In this note, we prove that if T has Property (F), then FredT (A) ? GL(A) = Fred0T (A) iff ltsr (J) = 1. .

Let be a unital Banach algebra. Assume that a has a generalized inverse a+. Then is said to be a stable perturbation of a if . In this paper we give various conditions for stable perturbation of a generalized invertible element and show that the equation is closely related to the gap function . These results will be applied to error estimates for perturbations of the Moore-Penrose inverse in C*–algebras and the Drazin inverse in Banach algebras.

We define the reduced minimum modulus \(\gamma _{\mathcal {A}} (a)\) of a nonzero element a in a unital C*-algebra \({\mathcal{A}}\) by \(\gamma _{\mathcal {A}} (a) = \rm{inf}\{\parallel a-b \parallel | \rm{AL}({\it a})\subsetneqq AL({\it b}), b \in {\mathcal {A}}\}\). We prove that \(\gamma _{\mathcal {A}} (a) = \rm{inf}\{\lambda | \lambda \in \sigma((a^{*}a)^{\frac{1}{2}})\setminus \{0\}\}\). Applying this result to \({\mathcal{A}}\) and its closed two side ideal \({\mathcal{I}}\), we get that dist \((a, \Phi^{c}_{l}({\mathcal {A}})) = \rm{min}\{\lambda | \lambda \in \sigma(\pi((a^{*}a)^{\frac{1}{2}}))\}\), \(\forall a \in {\mathcal {A}}\setminus \{0\}\) and \(\gamma _{\mathcal {B}}(\pi(a)) = \text{sup}\{\gamma _{\mathcal {A}}(a + k) | k \in {\mathcal {I}}\}\) for any \(a \in {\mathcal{A}}\setminus{\mathcal{I}}\) if RR\(({\mathcal{A}})\) = 0, where \({\mathcal{B}} = {\mathcal{A}}/{\mathcal{I}}\) and \(\pi : {\mathcal{A}} \rightarrow {\mathcal{B}}\) is the quotient homomorphism and \(\Phi^{c}_{l} ({\mathcal{A}}) =\{a \in {\mathcal {A}} | \pi(a) \text{is not left invertible in}\,{\mathcal {B}}\}\). These results generalize corresponding results in Hilbert spaces.

A unital C*-algebra A is said to have the (APD)-property if every nonzero element in A has the approximate polar decomposition. Let J be a closed ideal of A. Suppose that J and A/J have (APD). In this paper, we give a necessary and sufficient condition that makes A have (APD). Furthermore, we show that if RR(J) = 0 and tsr(A/J) = 1 or A/J is a simple purely infinite C*-algebra, then A has (APD).

Let X be a compact metric space and A be a unital simple C*-algebra with TR (A)=0. Suppose that ϕ : C(X) → A is a unital monomorphism. We study the problem when ϕ can be approximated by homomorphisms with finite-dimensional range. We give a K-theoretical necessary and sufficient condition for ϕ being approximated by homomorphisms with finite-dimensional range.

For any bounded linear operator A in a Banach space, two generalized condition numbers, k(A) and k(A) are defined in this paper. These condition numbers may be applied to the perturbation analysis for the solution of ill-posed differential equations and bounded linear operator equations in infinite dimensional Banach spaces. Different expressions for the two generalized condition numbers are discussed in this paper and applied to the perturbation analysis of the operator equation.

We show that if A is a unital C * -algebra with tracial topological rank r (and write TR(A) = r) and dimX = k, then TR(A ⊗ C(X)) ≤ r + k. Suppose that TR(B) = k. It is shown that TR(A ⊗ B) < r+k if both A and B are assumed to be simple, or B is an AH-algebra. Examples are also given, which show that the corresponding equality could not hold in general.

A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra \( {\user1{\mathcal{A}}} \) is a tracial limit of CTracial limit, Tracial topological rank*-algebras in \( {\user1{\mathcal{I}}}^{{{\left( k \right)}}} \) if and only if \( {\user1{\mathcal{A}}} \) has tracial topological rank no more than k. We present several known results using the notion of tracial limits.

We show that if $\mathcal A$ has tracial topological rank no more than k, then \[ {\rm U}_m (A)/{\rm U}^0_m ({\mathcal A})\cong K_1 ({\mathcal A})\ {\rm for}\ m\ge 1 +\left[ \frac{k}{2} \right] \] and if p, q ∈ A are two projections with [p] = [q] in $K_0 ({\mathcal A})$, then \[ {\rm diag} (p, 1_m)\sim {\rm diag} (q, 1_m)\ {\rm where}\ m =\max \left\{ 1, \left\{ \frac{k}{2} \right\} \right\}\,. \] Other results for K0(A) are also established.

Let L be a subspace of ${\bf R}^n$ and P L be the orthogonal projection of R n onto L . Then for the n × n matrix A , the generalized Bott-Duffin (B-D) inverse $A^{(+)}_{(L)}$ is given by $A^{(+)}_{(L)}=P_L(AP_L+I-P_L)^+$ . In this article we prove that $A^{(+)}_{(L)}=(P_LAP_L)^+$ iff $AL\cap L^\perp =0$ . This result extends the concept so-called the " L -s.p.d" matrix proposed by Chen in his article "The Generalized Bott-Duffin Inverse and its Applications". In the rest part of the article, the perturbation analysis of $A^{(+)}_{(L)}$ and the least squares solution of the systems $Ax+B^*y=b, Bx=d$ are established under certain small perturbation of A .

To evaluate the immunomodulatory properties of human amniotic mesenchymal stromal cells.Human amniotic mesenchymal stromal cells were isolated, characterized by flow cytometry, cultured in vitro, and evaluated in allogeneic and xenogeneic mixed lymphocyte reactions. The proliferation of T cells and the expression of interleukin 2 and interferon gamma by T cells were evaluated in the presence of human amniotic mesenchymal stromal cells.Human amniotic mesenchymal stromal cells were successfully isolated from human amniotic membranes and had well-defined human mesenchymal stem cell markers (CD90, CD73, CD105, and CD166). The human amniotic mesenchymal stromal cells inhibited the proliferation of human and rabbit T cells and the secretion of interleukin-2 and interferon gamma by human T cells.Human amniotic mesenchymal stromal cells may be useful for cell therapy and tissue engineering because of availability, phenotypic plasticity, and immunomodulatory properties.

In this paper, we have proven that for the Jordan blockS(θ) withS(θ) ∈ (SI), ⊕ =1 S(θ) =S(θ) (n) (n ≥ 1) has unique finite (SI) decomposition up to a similarity. As result, we obtain that ifV is a Volterra operator onH=L 2([0, 1]), thenV (n) has unique finite (SI) decomposition.

LetX1, X2be two Banach spaces over the complex fieldCand letT:X1 → X2be a bounded linear operator with the generalized inverseT+. Let T = T + δT be a bounded linear operator with ‖T+‖ ‖δT‖ dim ker T = dim ker T ∞ or R( T ) ∩ Ker T + = 0 . Then T has the generalized inverse T = (I + T + δT) −1 T + with ‖ T + ‖ ≤ ‖T + ‖ 1 − ‖T + ‖ ‖δT‖ . This result generalizes Theorem 3.9 of Na . Using this result, we give some results of the perturbation analysis for the operator equationTx = b.

BACKGROUND: To establish a novel method based on time‐resolved immunofluorometric assay (TR‐IFMA) with higher sensitivity and a broader detection range for detecting serum hepatitis B virus large surface protein (L protein). METHODS: The precision, sensitivity, specificity, coefficient of recovery, and stability of the assay were evaluated and comparison with the classical enzyme‐linked immunosorbent assay (ELISA) was also executed. RESULTS: The precision, specificity, and sensitivity of the TR‐IFMA were clearly better than ELISA. Particularly, the sensitivity was 0.1 ng/ml; moreover, the specificity was 100%, 96%, 92.5%, 96.9%, 97.8%, and 100% in the sera of healthy blood donors, systemic lupus erythematosus (SLE) patients, rheumatoid arthritis (RA) patients, hepatitis C virus (HCV) patients, cytomegalovirus (CMV) infection patients, and pregnant patients, respectively. Meanwhile, we observed that the established TR‐IFMA kit has a wider acceptable linear range of 0.63–10,367 ng/ml rather than the regular commercial ELISA kit having range of only 10.12–1095.9 ng/ml. Subsequently, correlation coefficient between the TR‐IFMA and ELISA was 0.8009. The intra‐ and interassay precision rates were less than 5% for three different concentrations. The average recovery rate for L protein was 101.17%. In sum, the established assay kit performed better in terms of stability than the commercial ELISA kit. CONCLUSION: The TR‐IFMA that we developed for L protein presented a higher sensitivity and wider detecting range than regular commercial ELISA. Therefore, this TR‐IFMA has promising value both in the screening of HBV and monitoring of antiviral therapy.

In this paper, we investigate the perturbation for the Moore-Penrose inverse of closed operators on Hilbert spaces. By virtue of a new inner product defined on $H$, we give the expression of the Moore-Penrose inverse $\bar{T}^\dag$ and the upper bounds of $\|\bar{T}^\dag\|$ and $\|\bar{T}^\dag -T^\dag\|$. These results obtained in this paper extend and improve many related results in this area., Comment: 9 pages

Let H 1 , H 2 be two Hilbert spaces over the same field, and let T : H 1 → H 2 be a bounded linear operator with closed range. We give a complete description of the perturbation analysis for the least squares solution to the operator equation T x = y , where x ∈ H 1 , y ∈ H 2 .

In this paper, we investigate the invertibility of $I_Y+\delta TT^+$ when $T$ is a closed operator from $X$ to $Y$ with a generalized inverse $T^+$ and $\delta T$ is a linear operator whose domain contains $D(T)$ and range is contained in $D(T^+)$. The characterizations of the stable perturbation $T+\delta T$ of $T$ by $\delta T$ in Banach spaces are obtained. The results extend the recent main results of Huang's in Linear Algebra and its Applications., Comment: 9 pages, accepted by Linear Algebra and its Applications

In this paper, the perturbation problems of $A_{T,S}^{(2)}$ are considered. By virtue of the gap between subspaces, we derive the conditions that make the perturbation of $A_{T,S}^{(2)}$ is stable when $T,S$ and $A$ have suitable perturbations. At the same time, the explicit formulas for perturbation of $A_{T,S}^{(2)}$ and new results on perturbation bounds are obtained., 13 pages, Electronic Journal of Linear Algebra (accepted)

In this short note, we prove that for a $C^*$-algebra $\aa$ generated by $n$ elements, $M_{k}(\tilde{\aa})$ is generated by $k$ mutually unitarily equivalent and almost mutually orthogonal projections for any $k\ge \de(n)=\min\big\{k\in\mathbb N\,|\,(k-1)(k-2)\ge 2n\big\}$. Then combining this result with recent works of Nagisa, Thiel and Winter on the generators of $C^*$--algebras, we show that for a $C^*$-algebra $\aa$ generated by finite number of elements, there is $d\ge 3$ such that $M_d(\tilde A)$ is generated by three mutually unitarily equivalent and almost mutually orthogonal projections. Furthermore, for certain separable purely infinite simple unital $C^*$--algebras and $AF$--algebras, we give some conditions that make them be generated by three mutually unitarily equivalent and almost mutually orthogonal projections., Comment: 10 pages

Let $\A$ be a unital separable nuclear $C^*$--algebra which belongs to the bootstrap category $\N$ and $\B$ be a separable stable $C^*$--algebra. In this paper, we consider the group $\Ext_u(\A,\B)$ consisting of the unitary equivalence classes of unital extensions $\tau\colon\A\rightarrow Q(\B)$. The relation between $\Ext_u(\A,\B)$ and $\Ext(\A,\B)$ is established. Using this relation, we show the half--exactness of $\Ext_u(\cdot,\B)$ and the (UCT) for $\Ext_u(\A,\B)$. Furthermore, under certain conditions, we obtain the half--exactness and Bott periodicity of $\Ext_u(\A,\cdot)$., Comment: 16 pages Acta Math. Sinica (English series)(to appear)

A hierarchy distributed route structure based on IPv6 address in peer to peer systems is proposed in order to solve the problems that physical topology and logical network does not match so as to inefficient search in distributed hash table at present. By building node identifier using IPv6 address and hashing different level clustering identifier to set up hierarchy route, near nodes in physical network are closer in overlay. Smaller hops across domain, lower search latency, and higher efficiency are proved.

Let $X$ be Banach space and let $T, \bar T=T+\delta T$ be bounded linear operators on $X$. Suppose that $T$ has the Drazin inverse $T^D$ and $\text{Ind} (T)=n$. In this paper, we show that if $\|\delta T\|$ is sufficiently small and $\text{Ran} (\bar T^n) \cap \text{Ker} (({T^D})^n) = \{0\}$, then $\bar T$ is Drazin invertible with $\text{Ind} (\bar T)\le n$. In this case, the expression of $\bar T^D$ is given and the upper bounds of $\|\bar T^D\|$ and $$\dfrac{\|\bar T^D-T^D\|}{\|T^D\|}$$ are established. If $\dim X

Let $0\to \mathcal J\to \mathcal A\to \mathcal A / \mathcal J\to 0$ be a short exact sequence of separable $C^*$-algebras. We introduce the notion of tracially quasidiagonal extension. Suppose that $\mathcal J$ and $\mathcal A/J$ have tracial topological rank zero. We prove that if $(\mathcal A, \mathcal J)$ is tracially quasidiagonal, then $\mathcal A$ has tracial topological rank zero.

Let H1,H2 be two Hilbert spaces over the complex field C and let T:H1 → H2 be a bounded linear operator with the generalized inverse T+. Let T = T + δT be a bounded linear operator with ∥T+∥ ∥δT∥ 〈 1. Suppose that dim ker T = dim ker T 〈 ∞ or R(T) ∩ R(T)⊥ = 0. Then T has the generalized inverse T+=[I−(I+T+δT)−1(I−T+T)−(I−T+)(I+T+δT)∗−1]1(1+δTT+)−1T+X[(I+δTT+)TT+)TT+(I+δTT+)−1+(I+δTT+)*ast;−1TT+(I+δTT+)∗−I]−1 with ‖T+‖⩽‖T+‖1−‖T+‖‖δT‖ This result gives an analogue of Theorem 3.9 of M.Z. Nashed (“Generalized Inverses and Applications”, Academic Press, New York, 1976) in Hilbert spaces.