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Orientation analysis of fibers is widely applied in the fields of medical, material and life sciences. The orientation information allows predicting properties and behavior of materials to validate and guide a fabrication process of materials with controlled fiber orientation. Meanwhile, development of detector systems for high-resolution non-invasive 3D imaging techniques led to a significant increase in the amount of generated data per a sample up to dozens of gigabytes. Though plenty of 3D orientation estimation algorithms were developed in recent years, neither of them can process large datasets in a reasonable amount of time. This fact complicates the further analysis and makes impossible fast feedback to adjust fabrication parameters. In this work, we present a new method for quantifying the 3D orientation of fibers. The GPU implementation of the proposed method surpasses another popular method for 3D orientation analysis regarding accuracy and speed. The validation of both methods was performed on a synthetic dataset with varying parameters of fibers. Moreover, the proposed method was applied to perform orientation analysis of scaffolds with different fibrous micro-architecture studied with the synchrotron μCT imaging setup. Each acquired dataset of size 600x600x450 voxels was analyzed in less 2 minutes using standard PC equipped with a single GPU. [ABSTRACT FROM AUTHOR]

Hybrid 3D scaffolds composed of different biomaterials with fibrous structure or enriched with different inclusions (i.e., nano- and microparticles) have already demonstrated their positive effect on cell integration and regeneration. The analysis of fibers in hybrid biomaterials, especially in a 3D space is often difficult due to their various diameters (from micro to nanoscale) and compositions. Though biomaterials processing workflows are implemented, there are no software tools for fiber analysis that can be easily integrated into such workflows. Due to the demand for reproducible science with Jupyter notebooks and the broad use of the Python programming language, we have developed the new Python package quanfima offering a complete analysis of hybrid biomaterials, that include the determination of fiber orientation, fiber and/or particle diameter and porosity. Here, we evaluate the provided tensor-based approach on a range of generated datasets under various noise conditions. Also, we show its application to the X-ray tomography datasets of polycaprolactone fibrous scaffolds pure and containing silicate-substituted hydroxyapatite microparticles, hydrogels enriched with bioglass contained strontium and alpha-tricalcium phosphate microparticles for bone tissue engineering and porous cryogel 3D scaffold for pancreatic cell culturing. The results obtained with the help of the developed package demonstrated high accuracy and performance of orientation, fibers and microparticles diameter and porosity analysis. [ABSTRACT FROM AUTHOR]

In view of the increasing competition in the market of rolled products, the problem of evaluation of the quality of strips in various stages of the process of rolling seems to be quite urgent. As the main geometric criteria of the quality of rolled strips, we can mention the cross-sectional profile of hot-rolled semifinished products and the plot of specific tension in the strips after cold rolling. We discuss the problems of formalization of measurements of the cross-sectional profiles, classification of hot-rolled profiles into characteristic types, and the influence of these criteria on the formation of the plots of specific tension in cold-rolled strips. [ABSTRACT FROM AUTHOR]

The recent developments in detector technology made possible 4D (3D + time) X-ray microtomographywith high spatial and time resolutions. The resolution and duration of such experiments is currently limited by destructive X-ray radiation. Algebraic reconstruction technique (ART) can incorporate a priori knowledge into a reconstruction model that will allow us to apply some approaches to reduce an imaging dose and keep a good enough reconstruction quality. However, these techniques are very computationally demanding. In this paper we present a framework for ART reconstruction based on OpenCL technology. Our approach treats an algebraic method as a composition of interacting blocks which performdifferent tasks, such as projection selection, minimization, projecting and regularization. These tasks are realised using multiple algorithms differing in performance, the quality of reconstruction, and the area of applicability. Our framework allows to freely combine algorithms to build the reconstruction chain. All algorithms are implemented with OpenCL and are able to run on a wide range of parallel hardware. As well the framework is easily scalable to clustered environment with MPI. We will describe the architecture of ART framework and evaluate the quality and performance on latest generation of GPU hardware from NVIDIA and AMD. [ABSTRACT FROM AUTHOR]

On-line monitoring of synchrotron 3D-imaging experiments requires very fast tomographic reconstruction. Direct Fourier methods (DFM) have the potential to be faster than standard Filtered Backprojection. We have evaluated multiple DFMs using various interpolation techniques. We compared reconstruction quality and studied the parallelization potential. A method using Direct Fourier Inversion (DFI) and a sinc-based interpolation was selected and parallelized for execution on GPUs. Several optimization steps were considered to boost the performance. Finally we evaluated the achieved performance for the latest generation of GPUs from NVIDIA and AMD. The results show that tomographic reconstruction with a throughput of more than 1.5 GB/sec on a single GPU is possible. [ABSTRACT FROM AUTHOR]

We consider a Sklyanin algebra S with 3 generators, which is the quadratic algebra over a field K with 3 generators x , y , z given by 3 relations p x y + q y x + r z z = 0 , p y z + q z y + r x x = 0 and p z x + q x z + r y y = 0 , where p , q , r ∈ K . This class of algebras enjoyed much of attention, in particular, using tools from algebraic geometry, Feigin, Odesskii [15] , and Artin, Tate and Van den Bergh [3] , showed that if at least two of the parameters p , q and r are non-zero and at least two of three numbers p 3 , q 3 and r 3 are distinct, then S is Koszul and has the same Hilbert series as the algebra of commutative polynomials in 3 variables. It became commonly accepted, that it is impossible to achieve the same objective by purely algebraic and combinatorial means, like the Gröbner basis technique. The main purpose of this paper is to trace the combinatorial meaning of the properties of Sklyanin algebras, such as Koszulity, PBW, PHS, Calabi–Yau, and to give a new constructive proof of the above facts due to Artin, Tate and Van den Bergh. Further, we study a wider class of Sklyanin algebras, namely the situation when all parameters of relations could be different. We call them generalized Sklyanin algebras. We classify up to isomorphism all generalized Sklyanin algebras with the same Hilbert series as commutative polynomials on 3 variables. We show that generalized Sklyanin algebras in general position have a Golod–Shafarevich Hilbert series (with exception of the case of field with two elements). [ABSTRACT FROM AUTHOR]

Abstract: Recently, Bès, Martin, and Sanders [11] provided examples of disjoint hypercyclic operators which fail to satisfy the Disjoint Hypercyclicity Criterion. However, their operators also fail to be disjoint weakly mixing. We show that every separable, infinite dimensional Banach space admits operators with which are disjoint weakly mixing, and still fail to satisfy the Disjoint Hypercyclicity Criterion, answering a question posed in [11]. Moreover, we provide examples of disjoint hypercyclic operators , whose corresponding set of disjoint hypercyclic vectors is nowhere dense, answering another question posed in [11]. In fact, we explicitly describe their set of disjoint hypercyclic vectors. Those same disjoint hypercyclic operators fail to be disjoint topologically transitive. Lastly, we create examples of two families of d-hypercyclic operators which fail to have any d-hypercyclic vectors in common. [Copyright &y& Elsevier]

We consider random nondirected networks subject to dynamics conserving vertex degrees and study, analytically and numerically, equilibrium three-vertex motif distributions in the presence of an external field h coupled to one of the motifs. For small h, the numerics is well described by the "chemical kinetics" for the concentrations of motifs based on the law of mass action. For larger h, a transition into some trapped motif state occurs in Erdos-Rényi networks. We explain the existence of the transition by employing the notion of the entropy of the motif distribution and describe it in terms of a phenomenological Landau-type theory with a nonzero cubic term. A localization transition should always occur if the entropy function is nonconvex. We conjecture that this phenomenon is the origin of the motifs' pattern formation in real evolutionary networks. [ABSTRACT FROM AUTHOR]

Abstract: By the Golod–Shafarevich theorem, an associative algebra R given by n generators and homogeneous quadratic relations is not 5-step nilpotent. We prove that this estimate is optimal. Namely, we show that for every positive integer n, there is an algebra R given by n generators and homogeneous quadratic relations such that R is 5-step nilpotent. [Copyright &y& Elsevier]

Abstract: We say that a (countably dimensional) topological vector space is orbital if there is and a vector such that is the linear span of the orbit . We say that is strongly orbital if, additionally, can be chosen to be a hypercyclic vector for . Of course, can be orbital only if the algebraic dimension of is finite or infinite countable. We characterize orbital and strongly orbital metrizable locally convex spaces. We also show that every countably dimensional metrizable locally convex space does not have the invariant subset property. That is, there is such that every non-zero is a hypercyclic vector for . Finally, assuming the Continuum Hypothesis, we construct a complete strongly orbital locally convex space. As a byproduct of our constructions, we determine the number of isomorphism classes in the set of dense countably dimensional subspaces of any given separable infinite dimensional Fréchet space . For instance, in , there are exactly 3 pairwise non-isomorphic (as topological vector spaces) dense countably dimensional subspaces. [Copyright &y& Elsevier]

Abstract: According to Grivaux, the group of invertible linear operators on a separable infinite dimensional Banach space acts transitively on the set of countable dense linearly independent subsets of . As a consequence, each is an orbit of a hypercyclic operator on . Furthermore, every countably dimensional normed space supports a hypercyclic operator. Recently Albanese extended this result to Fréchet spaces supporting a continuous norm. We show that for a separable infinite dimensional Fréchet space , acts transitively on if and only if possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator. [Copyright &y& Elsevier]

In chemical technology, an important place is occupied by studies of the processes of mass and heat transfer in moving media. Obviously, in order to study these processes, it is necessary to know how the media move. Determining the velocity field of liquids and gases is a purely kinematic task. Can it be solved without resorting to the equations of motion, limited only by the continuity equation? [ABSTRACT FROM AUTHOR]

A tuple (T 1, … , T n ) of commuting continuous linear operators on a topological vector space X is called hypercyclic if there is x ∈ X such that the orbit of x under the action of the semigroup generated by T 1, … , T n is dense in X. This concept was introduced by Feldman, who has raised seven questions on hypercyclic tuples. We answer four of those, which can be dealt with on the level of operators on finite dimensional spaces. In particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on ℂ n (respectively, on ℝ n ) is n + 1 (respectively, ), that there are non-diagonalizable tuples of operators on ℝ2 which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on ℂ3 such that every operator commuting with each member of the tuple is non-cyclic. [ABSTRACT FROM AUTHOR]

Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space ℓ1. We extend this result. In particular, we show that there is a hypercyclic operator on the locally convex direct sum of a sequence {Xn}n∈ℕ of Fréchet spaces if and only if each Xn is separable and there are infinitely many n∈ℕ for which Xn is infinite-dimensional. Moreover, we characterize inductive limits of sequences of separable Banach spaces which support a hypercyclic operator. [ABSTRACT FROM AUTHOR]

Abstract: We show that for every supercyclic strongly continuous operator semigroup acting on a complex -space, every with is supercyclic. Moreover, the set of supercyclic vectors of each with is exactly the set of supercyclic vectors of the entire semigroup. [Copyright &y& Elsevier]

Abstract: We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator T on a complex Fréchet space X and a set which is not of zero three-dimensional Lebesgue measure, the family has no common hypercyclic vectors. This allows to answer negatively questions raised by Godefroy and Shapiro and by Aron. We also prove a sufficient condition for a family of scalar multiples of a given operator on a complex Fréchet space to have a common hypercyclic vector. It allows to show that if and is non-constant, then the family has a common hypercyclic vector, where , , and , providing an affirmative answer to a question by Bayart and Grivaux. Finally, extending a result of Costakis and Sambarino, we prove that the family has a common hypercyclic vector, where acts on the Fréchet space of entire functions on one complex variable. [Copyright &y& Elsevier]

Abstract: A series is called a pointwise universal trigonometric series if for any , there exists a strictly increasing sequence of positive integers such that converges to pointwise on . We find growth conditions on coefficients allowing and forbidding the existence of a pointwise universal trigonometric series. For instance, if as for some , then the series cannot be pointwise universal. On the other hand, there exists a pointwise universal trigonometric series with as . [Copyright &y& Elsevier]

The article focuses on the use and implementation of the products of intellectual activity and its legal protection under Federal Law on Enforcing of the Civil Code of the Russian Federation or RF Civil Code. It discloses that the legal protection of the said products causes problems to defense enterprises and designers of armaments. It differentiates the author and the copyright holder, the methods of assessing the target analog, and the four groups of intellectual property protection.

Abstract: We prove that under certain topological conditions on the set of universal elements of a continuous map T acting on a topological space X, that the direct sum is universal, where is multiplication by a generating element of a compact topological group. We use this result to characterize -supercyclic operators and to show that whenever T is a supercyclic operator and are pairwise different non-zero complex numbers, then the operator is cyclic. The latter answers affirmatively a question of Bayart and Matheron. [Copyright &y& Elsevier]

Abstract: A complex number λ is called an extended eigenvalue of a bounded linear operator T on a Banach space if there exists a non-zero bounded linear operator X acting on such that . We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set . [Copyright &y& Elsevier]

Abstract: A bounded linear operator T acting on a Banach space is called weakly hypercyclic if there exists such that the orbit is weakly dense in and T is called weakly supercyclic if there is for which the projective orbit is weakly dense in . If weak density is replaced by weak sequential density, then T is said to be weakly sequentially hypercyclic or supercyclic, respectively. It is shown that on a separable Hilbert space there are weakly supercyclic operators which are not weakly sequentially supercyclic. This is achieved by constructing a Borel probability measure μ on the unit circle for which the Fourier coefficients vanish at infinity and the multiplication operator acting on is weakly supercyclic. It is not weakly sequentially supercyclic, since the projective orbit under M of each element in is weakly sequentially closed. This answers a question posed by Bayart and Matheron. It is proved that the bilateral shift on , , is weakly supercyclic if and only if and that any weakly supercyclic weighted bilateral shift on for is norm supercyclic. It is also shown that any weakly hypercyclic weighted bilateral shift on for is norm hypercyclic, which answers a question of Chan and Sanders. [Copyright &y& Elsevier]

Abstract: Bounded linear operators on separable Banach spaces algebraically similar to the classical Volterra operator V acting on are characterized. From this characterization it follows that V does not determine the topology of , which answers a question raised by Armando Villena. A sufficient condition for an injective bounded linear operator on a Banach space to determine its topology is obtained. From this condition it follows, for instance, that the Volterra operator acting on the Hardy space of the unit disk determines the topology of for any . [Copyright &y& Elsevier]

The multiplicative spectrum of a complex Banach space X is the class $$\mathcal{K}$$ ( X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras ( X, *) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with unity. Properties of multiplicative spectra are studied. In particular, we show that $$\mathcal{K}$$ ( X n ) consists of countable compact spaces with at most n nonisolated points for any separable, hereditarily indecomposable Banach space X. We prove that $$\mathcal{K}$$ ( C[0, 1]) coincides with the class of all metrizable compact spaces. [ABSTRACT FROM AUTHOR]

We prove that for any finite ultrametric space M and any infinite-dimensional Banach space B there exists an isometric embedding of M into B. [Copyright &y& Elsevier]

We prove that for any Hausdorff topological vector space E over the field R there exists A⊂E such that E is homeomorphic to a subset of A×R and A×R is homeomorphic to a subset of E. Using this fact we prove that E is monotonically normal if and only if E is stratifiable. [Copyright &y& Elsevier]

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x)=∫a(x,y)f(b(x,y))μ(dy) acting on functions $f:\; [u,\; v]\backslash rightarrow\; \{\backslash Bbb\; C\}$ (evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius–Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius–Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set $\{\backslash Bbb\; C\}\backslash setminus\; (-\backslash infty\; ,\; -1]$. Analyzing the spectrum of the Frobenius–Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Röpstorff asymptotic formula for the decay of correlations of the Gauss map. [ABSTRACT FROM AUTHOR]

We construct a bounded function H : l[SUB2] × l[SUB2] → [this text does not converted in ASCII.txt] with continuous Frèchet derivative such that for any q[SUB0]∈ l[SUB2] the Cauchy problem) [This text is not converted in ASCII.txt] has no solutions in any neighborhood of zero in [This text is not converted in ASCII.txt]. [ABSTRACT FROM AUTHOR]

We prove that the Frobenius-Perron operator U of the cusp map F:[-1,1] →[-1,1], F(x) = 1 -2 √χ (which is an approximation of the Poincaré section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any q ∈ (0,1) the spectrum of U in the Hardy space in the disk {z ∈ C:z-q < 1 + q} is the union of the segment [0,1] and some finite or countably infinite set of isolated eigenvalues of finite multiplicity. [ABSTRACT FROM AUTHOR]

Presents theorems on the continuous restrictions of linear operators. Infinite-dimensional Banach space; Separable infinite-dimensional Banach space; Topological vector spaces of algebraic dimension.

It is proved that for any f &isn; C[sup k](L, ...), where k ∈ N and L is a closed linear subspace of a nuclear Frechét space X, the function f can be extended to a function of class C[sup k-1] defined on the entire space X. It is also proved that for any f ∈ C[sup k](L, ...), where k ∈ ... ∪ {∞} and L is a closed linear subspace of a conjugate X of a nuclear Frechét space, the function f can be extended to a function of class C[sup k] defined on the entire space X. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace. [ABSTRACT FROM AUTHOR]

Studies the spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space. Inclusion of the singular continuous spectrum of the Liouville operator of quantum statistical physics in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian; Relation between the Liouville operator and its corresponding Hamiltonian.

We have developed a time-domain simulation of two-dimensional Fourier imaging in which the signal is represented by a finite Fourier series. Each term corresponds to a spin isochromat and has a coefficient that evolves in response to radiofrequency and gradient pulses, and periods of free precession. An explicit calculation is performed to derive the number of isochromats required to achieve a specified degree of precision, permitting accurate results to be obtained in an efficient fashion. With this, the time-domain signal throughout the entire experiment is calculated. The resulting time domain data is combined into the standard k-space matrix and yields an image after two-dimensional Fourier transformation. Multiple-shot sequences such as spin warp and single-shot experiments such as Burst are simulated in the same fashion. Our procedure makes no assumptions about transverse dephasing between pulses, so that complicated sequences of direct and stimulated echoes are correctly modeled. The influence of spin-spin and spin-lattice relaxation is included in a natural way. A number of artifacts can be quantitatively reproduced. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 419–426, 1997 [ABSTRACT FROM AUTHOR]

We present efficient evanescent coupling of single organic molecules to a gallium phosphide (GaP) subwavelength waveguide (nanoguide) decorated with microelectrodes. By monitoring their Stark shifts, we reveal that the coupled molecules experience fluctuating electric fields. We analyze the spectral dynamics of different molecules over a large range of optical powers in the nanoguide to show that these fluctuations are light-induced and local. A simple model is developed to explain our observations based on the optical activation of charges at an estimated mean density of 2.5×1022 m-3 in the GaP nanostructure. Our work showcases the potential of organic molecules as nanoscopic sensors of the electric charge as well as the use of GaP nanostructures for integrated quantum photonics. [ABSTRACT FROM AUTHOR]

Abstract: We give a short proof of existence of disjoint hypercyclic tuples of operators of any given length on any separable infinite dimensional Fréchet space. Similar argument provides disjoint dual hypercyclic tuples of operators of any length on any infinite dimensional Banach space with separable dual. [Copyright &y& Elsevier]

We report on cryogenic coupling of organic molecules to ring microresonators obtained by looping subwavelength waveguides (nanoguides). We discuss fabrication and characterization of the chip-based nanophotonic elements which yield a resonator finesse in the order of 20 when covered by molecular crystals. Our observed extinction dips from single molecules reach 22%, consistent with an expected enhancement factor of up to 11 for the molecular emission into the nanoguide. Future efforts will aim at efficient coupling of a handful of molecules via their interaction with a ring microresonator mode, setting the ground for the realization of quantum optical cooperative effects. [ABSTRACT FROM AUTHOR]

We measure the quantum fluctuations of a single acoustic mode in a volume of superfluid He that is coupled to an optical cavity. Specifically, we monitor the Stokes and anti-Stokes light scattered by a standing acoustic wave that is confined by the cavity mirrors. The intensity of these signals (and their cross-correlation) exhibits the characteristic features of the acoustic wave's zero-point motion and the quantum backaction of the intracavity light. While these features are also observed in the vibrations of solid objects and ultracold atomic gases, their observation in superfluid He opens the possibility of exploiting the remarkable properties of this material to access new regimes of quantum optomechanics. [ABSTRACT FROM AUTHOR]

Vibrational levels of the electronic ground states in dye molecules have not been previously explored at a high resolution in solid matrices. We present new spectroscopic measurements on single polycyclic aromatic molecules of dibenzoterrylene embedded in an organic crystal made of para-dichlorobenzene. To do this, we use narrow-band continuous-wave lasers and combine spectroscopy methods based on fluorescence excitation and stimulated emission depletion to assess individual vibrational linewidths in the electronic ground state at a resolution of ∼30 MHz dictated by the linewidth of the electronic excited state. In this fashion, we identify several exceptionally narrow vibronic levels with linewidths down to values around 2 GHz. Additionally, we sample the distribution of vibronic wavenumbers, relaxation rates, and Franck–Condon factors, in both the electronic ground and excited states for a handful of individual molecules. We discuss various noteworthy experimental findings and compare them with the outcome of density functional theory calculations. The highly detailed vibronic spectra obtained in our work pave the way for studying the nanoscopic local environment of single molecules. The approach also provides an improved understanding of the vibrational relaxation mechanisms in the electronic ground state, which may help create long-lived vibrational states for applications in quantum technology. [ABSTRACT FROM AUTHOR]

Presented in this paper are measurements of an optomechanical device in which various acoustic modes of a sample of superfluid helium couple to a fiber-based optical cavity. In contrast with recent work on the paraxial acoustic mode confined by the cavity mirrors (Kashkanova et alNat. Phys. 2016 (https://doi.org/10.1038/NPHYS3900)), we focus specifically on the acoustic modes associated with the helium surrounding the cavity. This paper provides a framework for understanding how the acoustic modes depend on device geometry. The acoustic modes are observed using the technique of optomechanically induced transparency/amplification. The optomechanical coupling to these modes is found to be predominantly photothermal. [ABSTRACT FROM AUTHOR]

We have implemented a trilayer technological approach to fabricate $$\mathrm {Nb}{-}\mathrm {Cu}_{0.47}\mathrm {Ni}_{0.53}{-} \mathrm {Nb}$$ superconducting phase inverters ( $$\pi $$ -junctions) with enhanced critical current. Within this technique, all three layers of the superconductor-ferromagnet-superconductor junction deposited in a single vacuum cycle that have allowed us to obtain $$\pi $$ -junctions with critical current density up to 20 kA/cm $$^2$$ . The value achieved is a factor of 10 higher than for the step-by-step method used in earlier works. Our additional experiments have shown that this difference is related to a bilayered CuNi/Cu barrier used in the case of the step-by-step technique and interlayer diffusion at the CuNi/Cu interface. We show that the interlayer diffusion can be utilized for fine tuning of the $$0{-}\pi $$ transition temperature of already fabricated junctions. The results obtained open new opportunities for the CuNi-based phase inverters in digital and quantum Josephson electronics. [ABSTRACT FROM AUTHOR]

In this Letter we study a system consisting of two nearly degenerate mechanical modes that couple to a single mode of an optical cavity. We show that this coupling leads to nearly complete (99.5%) hybridization of the two mechanical modes into a bright mode that experiences strong optomechanical interactions and a dark mode that experiences almost no optomechanical interactions. We use this hybridization to transfer energy between the mechanical modes with 40% efficiency. [ABSTRACT FROM AUTHOR]

The state of a system in classical mechanics can be uniquely reconstructed if we know the positions and the momenta of all its parts. In 1958 Pauli has conjectured that the same holds for quantum mechanical systems. The conjecture turned out to be wrong. In this paper we provide a new set of examples of Pauli pairs, being the pairs of quantum states indistinguishable by measuring the spatial location and momentum. In particular, we construct a new set of spatially localized Pauli pairs. [ABSTRACT FROM AUTHOR]

Abstract: The distribution of motifs in random hierarchical topological networks defined by nonsymmetric random block-hierarchical adjacency matrices, is constructed for the first time. According to the classification of U. Alon et al. of network superfamilies (Milo et al., 2004 ) by their motifs distributions, our artificial directed random hierarchical networks fall into the superfamily of natural networks to which the neuron networks belong. This is the first example of a class of “handmade” topological networks with the motifs distribution as in a special class of natural networks of essential biological importance. [Copyright &y& Elsevier]

Let 픐 be the Banach space of σ-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of 픐 is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon–Nikodým theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen–Wintner purity theorem for our decompositions. [ABSTRACT FROM AUTHOR]

Abstract: Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on , with , are obtained. The results apply not only to the Riemann–Liouville operator and to with , but also to operators of the form , where ϕ is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann–Liouville operator as well as the Volterra operator can be related to the Levin–Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy–Carleman theorem, are needed to analyze the behavior of the orbits of , where . The results are applied to the study of cyclic properties of , where ϕ is a holomorphic function at 0. [Copyright &y& Elsevier]

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems. [ABSTRACT FROM AUTHOR]

Cancer cells display heterogeneous genetic characteristics, depending on the tumor dynamic microenvironment. Abnormal tumor vasculature and poor tissue oxygenation generate a fraction of hypoxic tumor cells that have selective advantages in metastasis and invasion and often resist chemo- and radiation therapies. The genetic alterations acquired by tumors modify their biochemical pathways, which results in abnormal tumor metabolism. An elevation in glycolysis known as the "Warburg effect" and changes in lipid synthesis and oxidation occur. Magnetic resonance spectroscopy (MRS) has been used to study tumor metabolism in preclinical animal models and in clinical research on human breast, brain, and prostate cancers. This technique can identify specific genetic and metabolic changes that occur in malignant tumors. Therefore, the metabolic markers, detectable by MRS, not only provide information on biochemical changes but also define different metabolic tumor phenotypes. When combined with the contrast-enhanced Magnetic Resonance Imaging (MRI), which has a high sensitivity for cancer diagnosis, in vivo magnetic resonance spectroscopic imaging (MRSI) improves the diagnostic specificity of malignant human cancers and is becoming an important clinical tool for cancer management and care. This article reviews the MRSI techniques as molecular imaging methods to detect and quantify metabolic changes in various tumor tissue types, especially in extracranial tumor tissues that contain high concentrations of fat. MRI/MRSI methods have been used to characterize tumor microenvironments in terms of blood volume and vessel permeability. Measurements of tissue oxygenation and glycolytic rates by MRS also are described to illustrate the capability of the MR technology in probing molecular information non-invasively in tumor tissues and its important potential for studying molecular mechanisms of human cancers in physiological conditions. [ABSTRACT FROM AUTHOR]

As moist gas enters a reciprocating compressor in the course of the operation of the compressor, heating of the gas depends on the degree of dryness of the gas and the rate of evaporation of the liquid droplets in the gas as well as on the coefficient of thermal conductivity of the moist gas and on the coefficient of heat transfer from the walls of the compressor cylinder to the gas. However, once the rotational speed of the compressor shaft reaches 300 min–1, the length of the gas intake process falls to one-tenth the length of the period of total evaporation of the droplets, hence the process of evaporation begins to exert a practical influence on the temperature of the gas. The gas temperature increases substantially due to the increase in the thermal conductivity coefficient of the moist gas and in the coefficient of heat transfer from the walls of the compressor cylinder to the gas. With a decrease in the degree of dryness of the gas from 1.0 to 0.6, preheating of the gas grows 7–8-fold, which leads to a reduction in the density of the gas in the filled work space of the cylinder and, as a consequence, to a decrease in the adiabatic efficiency of the compressor ηi by 14–16%, and this must be taken into account in the management of the production process. [ABSTRACT FROM AUTHOR]

Silicon-vacancy (SiV) color centers in diamond offer a promising system for quantum information applications owing to their intense narrowband emission and optically detectable spin states. Here, the fluorescent properties of ensembles and single SiV centers in diamonds obtained by high-pressure high-temperature synthesis from adamantane (below referred to as adamantane diamonds) are investigated at liquid-helium temperatures. Ensembles of SiV centers (~103) are studied in large diamond crystals (1–2 µm in size). Despite the large number of excited centers, the fine structure of the zero-phonon line, corresponding to four allowed optical transitions between the ground- and excited-state doublets of the SiV center, can be observed in the fluorescence spectra of these crystals. The width of individual lines is in the range of 60–80 GHz, which is explained by their inhomogeneous broadening. Single SiV centers are studied in diamond crystallites with sizes of about 200 nm. The width of the narrowest transition lines observed in the fluorescence spectra of single SiV centers under resonant excitation is almost three orders of magnitude smaller than linewidths in the spectra of SiV ensembles and is as small as 94 MHz; i.e., these lines are so narrow that their width is determined by the lifetime of the upper state of the transition. Therefore, adamantane nanodiamond features the narrowest emission line width of a single SiV center at cryogenic temperatures among other types of SiV-con-taining nanodiamonds of similar sizes obtained by the high-pressure high-temperature and chemical vapor deposition techniques. [ABSTRACT FROM AUTHOR]