Narrow Results

Based on the fact that, for a subfactor N of a II₁ factor M, the first nontrivial Jones index is two and then M is decomposed as the crossed product of N by an outer action of ℤ₂, we study pairs {N, uNu*} from the view-point of entropy for two subalgebras of M in connection with the entropy for automorphisms, where the inclusion of II₁ factors N ⊂ M is given with M being the crossed product of N by a finite group of outer automorphisms and u is a unitary in M.

UHF flows are the flows obtained as inductive limits of flows on full matrix algebras. We will revisit universal UHF flows and give an explicit construction of such flows on a UHF algebra M_k^∞ for any k and also present a characterization of such flows. Those flows are UHF flows whose cocycle perturbations are almost conjugate to themselves.

In order to give numerical characterizations of the notion of "mutual orthogonality", we introduce two kinds of family of positive definite matrices for a unitary u in a finite von Neumann algebra M. They are arising from u naturally depending on the decompositions of M. One corresponds to the tensor product decomposition and the other does to the crossed product decomposition. By using the von Neumann entropy for these positive definite matrices, we characterize the notion of mutual orthogonality between subalgebras.

In the paper, the mixing property of ℤ² subshift of finite type (SFT) is studied, some checkable conditions are provided to examine the property of mixing. Once the mixing property is checked, a class of examples can be found to show it possesses an entropy conjugacy property proposed in [Quas & Trow, 2000]. Finally, we construct an example of two shift spaces X and Y that are entropy conjugate but not conjugate.

We define a new invariant of a conjugacy class of subgroups which we call the breadth and prove that a quasiconvex subgroup of a negatively curved group has finite breadth in the ambient group. Utilizing the coset graph and the geodesic core of a subgroup we give an explicit algorithm for constructing a finite generating set for an intersection of a quasiconvex subgroup of a negatively curved group with its conjugate. Using that algorithm we construct algorithms for computing the breadth, the width, and the height of a quasiconvex subgroup of a negatively curved group. These algorithms decide if a quasiconvex subgroup of a negatively curved group is almost malnormal in the ambient group. We also explicitly compute a quasiconvexity constant of the intersection of two quasiconvex subgroups and give examples demonstrating that height, width, and breadth are different invariants of a subgroup.

We describe subgroups and overgroups of the generalized Thompson groups $V_n$ which arise via conjugation by rational homeomorphisms of Cantor space. We specifically consider conjugating $V_n$ by homeomorphisms induced by synchronizing transducers and their inverses. Our descriptions of the subgroups and overgroups use properties of the conjugating transducer to either restrict or augment the action of $V_n$ on Cantor space. We also consider a class $𝔓$ of transducers containing all invertible, initial transducers. We associate to every transducer $T$ in this class, a group ${\mathscr{H}}(T)$. We show that for a certain subclass of $𝔓$, the groups ${\mathscr{H}}(T)$ are simple.

We study the structure of nilpotent subsemigroups in the semigroup M(n,𝔽) of all n×n matrices over a field 𝔽 with respect to the operation of the usual matrix multiplication. We describe the maximal subsemigroups among the nilpotent subsemigroups of a fixed nilpotency degree and classify them up to isomorphism. We also describe isolated and completely isolated subsemigroups and conjugated elements in M(n,𝔽).

We give a clear description of the solution set to the quaternion matrix equation , where A, B are known, X is unknown and denotes the usual conjugate of X.

meso-Tris(3,5-di-tert-butylphenyl)porphyrin (P-H) is bonded with L-phenylalanine (H-Phe-OH) directly at the unsubstituted meso-position of the former and the p-position of phenyl group of the latter to afford chiral porphyrin-amino acid conjugate H-Phe(p-P)-OH. The N-(9-fluorenyl)-methyloxycarbonyl compound, Fmoc-Phe(p-P)-OH, was synthesized without any loss of enantiomeric purity (based on chiral HPLC analysis) from commercially available L-tyrosine and was useful for preparation of the peptides in both liquid and solid phases. Other meso-tetraarylporphyrins possessing multi-amino acid moieties are reported, as well as achiral porphyrin-amino acids readily prepared and their dipeptidyl porphyrin dyads.

An unsymmetrical phthalocyanine based one- and two-photon fluorescence imaging probe that substituted with 4-tert-butylphenoxy and RDGyK moieties was developed and characterized by UV-vis and high-resolution MALDI-TOF/MS. The conjugate is non-aggregated in $N$,$N$-dimethylformamide, with relatively weak fluorescence emission (${\mathrm{\Phi }}_F=$ 0.023) and high singlet oxygen quantum yield (${\mathrm{\Phi }}_{\mathrm{\Delta }}=$ 0.55). Conjugation of the cyclic peptide sequence c(RGDyK) can enhance the cellular uptake towards the DU145 and PC3 cells. While the fluorescence is greatly enhanced in mitochondria, the conjugate is non-cytotoxicity either in dark or upon exposure to red-light with dose up to 12 J.cm${}^{-2}$. The results suggest that this conjugate is a promising multifunctional imaging probe for mitochondria and cancer.

Two mono meso-functionalized [20]di-$p$-benzihomoporphyrins containing $p$-formylphenyl and $p$-iodophenyl groups at meso-position respectively were synthesized by condensing one equivalent of appropriate tetrapyrrane with one equivalent of $p$-formyl benzaldehyde/$p$-iodo benzaldehyde in CH₂Cl₂ under mild acid catalyzed conditions. The meso-formylphenyl and meso-iodophenyl functionalized di-$p$-benzihomoporphyrins were used to synthesize two covalently linked di-$p$-benzihomoporphyrins-BODIPY conjugates. The meso-formylphenyl-functionalized di-$p$-benzihomoporphyrin was converted to corresponding meso-dipyrrolyl substituted di-$p$-benzihomoporphyrin by treating with excess pyrrole under acid catalyzed conditions. In the next step, the meso-dipyrrolyl di-$p$-benzihomoporphyrin was subjected to oxidation followed by BF₂ complexation to afford the directly linked di-$p$-benzihomoporphyrin-BODIPY conjugate. The meso-iodophenyl functionalized di-$p$-benzihomoporphyrin was coupled with ethynyl-functionalized BODIPY under mild Pd(0) coupling condition to synthesize diphenylethyne-bridged di-$p$-benzihomoporphyrin-BODIPY conjugate. The two conjugates were characterized by HR-MS, NMR, absorption, electrochemical, fluorescence and DFT studies. The spectral and electrochemical studies indicated that the two constituents, di-$p$-benzihomoporphyrin and BODIPY units in the conjugates interact weakly and retain their individual characteristic features. DFT studies indicated a possibility of charge transfer between di-$p$-benzihomoporphyrin and BODIPY units in conjugates.

Background and Aims: Accurate endoscopic detection of premalignant lesions and early cancers in the colon is essential for cure, since prognosis is closely related to lesion size and stage. Although it has great clinical potential, autofluorescence endoscopy has limited tumor-to-normal tissue image contrast for detecting small preneoplastic lesions. We have developed a molecularly specific, near-infrared fluorescent monoclonal antibody (CC49) bioconjugate which targets tumor-associated glycoprotein 72 (TAG72), as a contrast agent to improve fluorescence-based endoscopy of colon cancer. Methods: The fluorescent anti-TAG72 conjugate was evaluated in vitro and in vivo in athymic nude mice bearing human colon adenocarcinoma (LS174T) subcutaneous tumors. Autofluorescence, a fluorescent but irrelevant antibody and the free fluorescent dye served as controls. Fluorescent agents were injected intravenously, and in vivo whole body fluorescence imaging was performed at various time points to determine pharmacokinetics, followed by ex vivo tissue analysis by confocal fluorescence microscopy and histology. Results: Fluorescence microscopy and histology confirmed specific LS174T cell membrane targeting of labeled CC49 in vitro and ex vivo. In vivo fluorescence imaging demonstrated significant tumor-to-normal tissue contrast enhancement with labeled-CC49 at three hours post injection, with maximum contrast after 48 h. Accumulation of tumor fluorescence demonstrated that modification of CC49 antibodies did not alter their specific tumor-localizing properties, and was antibody-dependent since controls did not produce detectable tumor fluorescence. Conclusions: These results show proof-of-principle that our near-infrared fluorescent-antibody probe targeting a tumor-associated mucin detects colonic tumors at the molecular level in real time, and offer a basis for future improvement of image contrast during clinical fluorescence endoscopy.