Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean {\it coordinate} system (X$^i$,$\tau$) as the quantum statistical system of N quantum (statistical) variables (X$^i$) and one {\it Euclidean time} variable ($\tau$). Introducing paths (lines or hypersurfaces) in this space (X$^i$,$\tau$), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the {\it mechanical} system. The system Hamiltonian appears as the {\it area}. We show quantization is realized by the {\it minimal area principle} in the present geometric approach. When we take a {\it line} as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a {\it hyper-surface} as the path, the system Hamiltonian is given by the {\it area} of the {\it hyper-surface} which is defined as a {\it closed-string configuration} in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.Comment: 20 pages, 8 figures, Proceedings of ICFS2010 (2010.9.13-18, Ise-Shima, Mie, Japan

Moment inversion problem for piecewise D-finite functions

We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation with polynomial coefficients on each continuity interval. Therefore, they may be specified by a finite amount of information. This reconstruction problem has practical importance in Signal Processing and other applications. It is somewhat of a ``folklore'' that the sequence of the moments of such ``piecewise D-finite''functions satisfies a linear recurrence relation of bounded order and degree. We derive this recurrence relation explicitly. It turns out that the coefficients of the differential operator which annihilates every piece of the function, as well as the locations of the discontinuities, appear in this recurrence in a precisely controlled manner. This leads to the formulation of a generic algorithm for reconstructing a piecewise D-finite function from its moments. We investigate the conditions for solvability of the resulting linear systems in the general case, as well as analyze a few particular examples. We provide results of numerical simulations for several types of signals, which test the sensitivity of the proposed algorithm to noise

Comparison of Ce( iv )/Th( iv )-alkynyl complexes and observation of a trans -influence ligand series for Ce( iv )

Organometallic cerium(iv) complexes have been challenging to isolate and characterize due to the strongly oxidizing nature of the cerium(iv) cation. Herein, we report two cerium(iv) alkynyl complexes, [Ce(TriNOx)(C[triple bond, length as m-dash]C-SiMe3)] (1-CeTMS) and [Ce(TriNOx)(C[triple bond, length as m-dash]C-Ph)] (1-CePh) (TriNOx3- = tris(2-tert-butylhydroxylaminato)benzylamine), that include terminal alkyne moieties. The isostructural thorium analogue [Th(TriNOx)(C[triple bond, length as m-dash]C-SiMe3)] (1-ThTMS) was also synthesized and compared with 1-CeTMS in bond distance, 13C-NMR spectra, vibrational spectra and electronic structure. The Ce-C bond distances were 2.501(3) Å for 1-CePh and 2.513(5) Å for 1-CeTMS on the shorter end of the few reported CeIV-C single bonds (2.478(3)-2.705(2) Å), possibly indicating significant Ce 5d- and 4f-orbital involvement. 13C-NMR spectroscopy was also consistent with Ce-C covalency, with significantly deshielded resonances ranging from 185-213 ppm. Such 13C-NMR shifts demonstrate a strong influence from spin-orbit coupling (SOC) effects, corroborated by computational studies. Raman analysis showed ν C[triple bond, length as m-dash]C stretching frequencies of 2000 cm-1 (1-CeTMS) and 2052 cm-1 (1-CePh), indicating the cerium(iv)-alkynyl interaction, compared to the parent HC[triple bond, length as m-dash]CPh (IR = 2105 cm-1 and Raman = 2104 cm-1). L3-edge X-ray absorption measurements revealed a predominant Ce(iv) electronic configuration, and magnetic measurements revealed temperature-independent paramagnetism. Electrochemical studies similarly revealed the electron donating ability of the alkynyl ligands, stronger than either fluoride or imido ligands for the Ce(iv)(TriNOx)-framework, with a cerium(iv/iii) reduction potential of E pc = -1.58 to -1.66 V vs. Fc/Fc+. Evidence for a trans-influence has been observed by evaluating a series including previously reported [CeIV(TriNOx)X]+/0 complexes with axial ligands X = THF, I-, Br-, Cl-, F-, -C[triple bond, length as m-dash]C-Ph, -C[triple bond, length as m-dash]C-SiMe3, -NH(3,5-(CF3)2-Ar), -OSiPh3, -N(M(L))(3,5-(CF3)2-Ar) [M(L) = Li(TMEDA), K(DME)2 or Cs(2,2,2-crypt)]. These data stand in contrast with previous reports of an inverse trans-influence at cerium(iv) and point to differences in involvement of cerium 4f- versus 5d-orbitals in the electronic structures of the complexes

Synthesis and Characterization of Solvated and Base-Free Cerium(III) Mixed-Sandwich Complexes

A series of solvated complexes: [(C8H8)Ln(C5Me4R)(DME)] Ln = La, R = -Me; (La-2) Ln = Ce, R = -Me, -SiMe3, -H; (Ce-2, Ce-3, Ce-4), [(dbCOT)Ln(C5Me5)(DME)] (Ln-6), (dbCOT2- = dibenzocyclooctadienide; Ln = Ce, La), [(dbCOT)Ce(C5Me4H)(DME)] (Ce-7) and [(hdcCOT)Ce(C5Me5)(DME)] (Ce-8) (hdcCOT2- = hexahydrodicyclopentacyclooctatetraenide) and base-free mixed-sandwich complexes [(C8H8)Ce(C5Me5)] (Ce-9), [(C8H8)Ce(C5Me4H) (Ce-10) and [(hdcCOT)Ce(C5Me5)] (Ce-11) of the early lanthanide metals cerium and lanthanum comprising variable cyclopentadienide (Cp-) and cyclooctatetraenide (COT2-) ligands is described. To evaluate the effect of cyclopentadienide and cyclooctatetraenide ligands on the characteristics of these complexes, their solid-state structural, electrochemical, and photophysical properties were studied and accompanied by theoretical calculations. To further evaluate the effect of ligands on the topology of the complexes and the reducing properties of the complexes, syntheses of several base-free congeners were pursued, which led to isolation of the first base-free monomeric and polymeric Ce(III) mixed-sandwich compounds

4f-orbital covalency enables a single-crystal-to-single-crystal ring-opening isomerization in a CeIV–cyclopropenyl complex

Metal-ligand bonding interactions for f-element compounds are typically highly polarized with only minor covalent character. Whereas the 5d/6d orbitals are known to be chemically accessible for dative bonding, recent quantum chemical and spectroscopic analyses have indicated appreciable 4f/5f-orbital involvement in certain metal-ligand bonds. However, 4f-orbital covalency has not been compellingly linked to distinctive modes of chemical reactivity via rigorous comparative study and mechanistic investigation. Here a series of MIV-cyclopropenyl complexes (M = Ti, Zr, Ce, Hf, Th) are described, wherein the cerium congener exhibits a 4f-covalent Ce=Cα interaction, causing a ring-opening isomerization reaction through a single-crystal-to-single-crystal transformation. The results provide evidence for 4f-orbital covalency by demonstrating its expression in the reactivity of an f-element complex within an isostructural series of tetravalent d- and f-block metal complexes. They also provide new directions for the study of orbital covalency effects of molecular compounds in solid-state chemical transformations

Non-Agonistic Bivalent Antibodies That Promote c-MET Degradation and Inhibit Tumor Growth and Others Specific for Tumor Related c-MET

The c-MET receptor has a function in many human cancers and is a proven therapeutic target. Generating antagonistic or therapeutic monoclonal antibodies (mAbs) targeting c-MET has been difficult because bivalent, intact anti-Met antibodies frequently display agonistic activity, necessitating the use of monovalent antibody fragments for therapy. By using a novel strategy that included immunizing with cells expressing c-MET, we obtained a range of mAbs. These c-MET mAbs were tested for binding specificity and anti-tumor activity using a range of cell-based techniques and in silico modeling. The LMH 80 antibody bound an epitope, contained in the small cysteine-rich domain of c-MET (amino acids 519–561), that was preferentially exposed on the c-MET precursor. Since the c-MET precursor is only expressed on the surface of cancer cells and not normal cells, this antibody is potentially tumor specific. An interesting subset of our antibodies displayed profound activities on c-MET internalization and degradation. LMH 87, an antibody binding the loop connecting strands 3d and 4a of the 7-bladed β-propeller domain of c-MET, displayed no intrinsic agonistic activity but promoted receptor internalization and degradation. LMH 87 inhibited HGF/SF-induced migration of SK-OV-3 ovarian carcinoma cells, the proliferation of A549 lung cancer cells and the growth of human U87MG glioma cells in a mouse xenograft model. These results indicate that c-MET antibodies targeting epitopes controlling receptor internalization and degradation provide new ways of controlling c-MET expression and activity and may enable the therapeutic targeting of c-MET by intact, bivalent antibodies

Review of the methods of determination of directed connectivity from multichannel data

The methods applied for estimation of functional connectivity from multichannel data are described with special emphasis on the estimators of directedness such as directed transfer function (DTF) and partial directed coherence. These estimators based on multivariate autoregressive model are free of pitfalls connected with application of bivariate measures. The examples of applications illustrating the performance of the methods are given. Time-varying estimators of directedness: short-time DTF and adaptive methods are presented

Uranium Nitrogen Multiple Bonding: Isostructural Anionic, Neutral, and Cationic Uranium Nitride Complexes Featuring a Linear U=N=U Core

Reaction of the uranium(III) tris(anilide) complex (THF)U(N[t-Bu]Ar)3 (1, THF = tetrahydrofuran; Ar = 3,5-Me2C6H3) with MN3 (M = Na, [N(n-Bu)4]) results in the formation of the bimetallic diuranium(IV/IV) complexes M[(μ-N)(U(N[t-Bu]Ar)3)2] (M[3]), which feature a single nitride ligand engaged as a linear, symmetric bridge between two uranium centers. The stability of the U=N=U core across multiple charge states is illustrated by stepwise chemical oxidation of Na[3] to the diuranium(IV/V) complex (μ-N)(U(N[t-Bu]Ar)3)2 (3) and the diuranium(V/V) complex [(μ-N)(U(N[t-Bu]Ar)3)2][B(ArF)4] {[3][B(ArF)4]; ArF= 3,5-(CF3)2C6H3}. M[3], 3, and [3]B(ArF)4] were characterized by NMR spectroscopy. single-crystal X-ray diffraction, and elemental analysis. The cyclic voltammogram of 3 reveals two clean, reversible one-electron electrochemical events at E1/2 = 1.69 and -0.67 V, assigned to the [3]-/3 and 3/[3]+ redox couples. respectively. The X-ray crystal structures of [N(n-Bu)4][3], 3, and [3][B(ArF)4] reveal a linear U=N=U core that contracts by only ∼ 0.03 Å across the [3]n (n = -1, 0, +1) series, an effect that is rationalized as being primarily electrostatic in origin. [3][B(ArF)4] reacts with NaCN, eliminating Na[B(ArF)4] and forming the known diuranium(IV/IV) cyanoimide complex ([μ-NCN)(U(N[t-Bu]Ar)3)2, suggesting that the U=N=U core has metallonitrene-like character.</p

Seizure prediction : ready for a new era

Acknowledgements: The authors acknowledge colleagues in the international seizure prediction group for valuable discussions. L.K. acknowledges funding support from the National Health and Medical Research Council (APP1130468) and the James S. McDonnell Foundation (220020419) and acknowledges the contribution of Dean R. Freestone at the University of Melbourne, Australia, to the creation of Fig. 3.Peer reviewe