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Confucius and American Democracy

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China Today 2024年第6期73卷 48-50页

作者： alfred.HORNUNG The Obama Institute for Transnational American Studies Johannes Gutenberg UniversityMainzGermany

UPON the establishment of European universities in the Middle Ages,the educational system in Western countries became characterized by an essentially Eurocentric *** was reflected in the study of Latin and Greek in high school,and in basing public life and political systems on philosophies of classical *** work of the influential Chinese philosopher Confucius(551-479 B.C.),a near-contemporary of the major Greek philosophers Socrates(469-399 B.C.),Plato(428-348 B.C.)and Aristotle(384-322 B.C.),whose ethical and political ideas entered into the constitutions of European states,remained unknown.

关键词： Latin Middle Confucius

Optic Axes and Elliptic Cone Equation in Coordinate-Invariant Treatment

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Journal of Modern Physics 2022年第6期13卷 1001-1043页

作者： alfred.Wünsche Institut für Physik Humboldt-Universit&auml t Newtonstr Berlin Germany

We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.

关键词： Permittivity Tensor Principal Permittivities Three-Dimensional Operator of Wave Equation Operator Invariants Refraction Vector Ray Vector Cone Ap-proximation in Neighborhood of Optic Axis Conical Refraction

Mathematical Aspects of SU (2) and SO(3,R) Derived from Two-Mode Realization in Coordinate-Invariant Form

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Journal of Modern Physics 2023年第3期14卷 361-413页

作者： alfred.Wünsche Institut für Physik Humboldt-Universit&#228t Newtonstr. 15 Berlin Germany

Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.

关键词： Boson Operators Lie Algebra Root Diagram Invariant Integration Hamilton-Cayley Identity Cayley-Gibbs-Fyodorov Parametrization Composition Law Quaternion Stereographic Projection Fractional Linear Transformation

Two Concepts in Optics of Anisotropic Dispersive Media and Polariton Case in Coordinate-Invariant Way

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Journal of Modern Physics 2022年第4期13卷 574-619页

作者： alfred.Wünsche Institut für Physik Humboldt-Universit&auml t Berlin Germany

Two concepts of phenomenological optics of homogeneous, anisotropic and dispersive media are compared, the younger and more general concept of media with spatial dispersion and the older concept of (bi)-anisotropic media with material tensors for electric and magnetic induction which only depend on the frequency. The general algebraic form of the polarization vectors for the electric field and their one-dimensional projection operators is discussed without the degenerate cases of optic axis for which they become two-dimensional projection operators. Group velocity and diffraction coefficients in an approximate equation for the slowly varying amplitudes of beam solutions are calculated. As special case a polariton permittivity for isotropic media with frequency dispersion but without losses is discussed for the usual passive case and for the active case (occupation inversion of two energy levels that goes in direction of laser theory) and the group velocity is calculated. For this active case, regions of frequency and wave vector with group velocities greater than that of light in vacuum were found. This is not fully understood and due to large diffraction is likely only to realize in guided resonator form. The notion of “negative refraction” is shortly discussed but we did not find agreement with its assessment in the original paper.

关键词： Spatial and Frequency Dispersion Bi-Anisotropic Media Uniaxial Media Passive and Active Media Negative Refraction Operator Invariants Complementary Operator Group Velocity

Approach to a Proof of the Riemann Hypothesis by the Second Mean-Value Theorem of Calculus

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Advances in Pure Mathematics 2016年第13期6卷 972-1021页

作者： alfred.Wünsche Humboldt-Universitü t Berlin Institut für Physik Nichtklassische Strahlung (MPG) Berlin Germany

By the second mean-value theorem of calculus (Gauss-Bonnet theorem) we prove that the class of functionswith an integral representation of the form with a real-valued function which is non-increasing and decreases in infinity more rapidly than any exponential functions , possesses zeros only on the imaginary axis. The Riemann zeta function as it is known can be related to an entire functionwith the same non-trivial zeros as . Then after a trivial argument displacement we relate it to a function with a representation of the form where is rapidly decreasing in infinity and satisfies all requirements necessary for the given proof of the position of its zeros on the imaginary axis z=iy by the second mean-value theorem. Besides this theorem we apply the Cauchy-Riemann differential equation in an integrated operator form derived in the Appendix B. All this means that we prove a theorem for zeros of on the imaginary axis z=iy for a whole class of function which includes in this way the proof of the Riemann hypothesis. This whole class includes, in particular, also the modified Bessel functions for which it is known that their zeros lie on the imaginary axis and which affirms our conclusions that we intend to publish at another place. In the same way a class of almost-periodic functions to piece-wise constant non-increasing functions belong also to this case. At the end we give shortly an equivalent way of a more formal description of the obtained results using the Mellin transform of functions with its variable substituted by an operator.

关键词： Riemann Hypothesis Riemann Zeta Function Xi Function Gauss-Bonnet Theorem Mellin Transformation

Overview of microRNAs as liquid biopsy biomarkers for colorectal cancer sub-type profiling and chemoresistance

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Cancer Drug Resistance 2021年第4期4卷 934-945页

作者： alfred.Buhagiar Elisa Seria Miriana Borg Joseph Borg Duncan Ayers Faculty of Medicine and Surgery University of MaltaMsida 2080Malta Centre for Molecular Medicine and Biobanking University of MaltaMsida 2080Malta Faculty of medical sciences Newcastle UniversityNewcastle upon Tyne NE17RUUK Faculty of Health Sciences University of MaltaMsida 2080Malta Faculty of Biology Medicine and Health SciencesThe University of ManchesterManchester M139PLUK

Colorectal cancer(CRC)is the third most common cancer *** has also been demonstrated that over the last ten years the incidence of CRC among younger people below the age of 50 is also *** for colorectal cancer is of utmost importance;the rationale behind screening is to target the malignancy and reduce the incidence and mortality of the *** methods to screen for incidence or relapse are therefore a requisite to detect cancer as early as *** findings demonstrate that many deaths are due to lack of screening and therefore early identification will lead to greater *** colorectal cancer,diagnostic tests include liquid biopsy *** the discovery of microRNAs(miRNAs),many studies have demonstrated the relationship between miRNAs and the various sub-types of *** miRNAs have been identified after analysing serum or plasma samples in patients,and such miRNAs were found to be significantly *** findings place the possibility of miRNAs to be at the epicentre of novel diagnostic techniques for CRC identification and sub-type stratification,including other characteristics associated with CRC development such as patient *** following review serves to underline the latest findings for miRNAs with such potential for routine diagnostic employment in CRC diagnostics and treatments.

关键词： MicroRNA miRNA liquid biopsy biomarkers colorectal cancer cancer

Boundary Conditions for Sturm-Liouville Equation with Transition Regions and Barriers or Wells

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Advances in Pure Mathematics 2021年第4期11卷 254-295页

作者： alfred.Wünsche Institut für Physik Humboldt-Universit&#228 t Nonclassical Radiation Berlin Germany

By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or wells between two asymptotic potentials for which the solutions are supposed as known. We call such expansions “moment series” because the coefficients are determined by moments of the function. An infinite system of boundary conditions is obtained and it is shown how by truncation it can be reduced to approximations of a different order (explicitly made up to third order). Reflection and refraction problems are considered with such approximations and also discrete bound states possible in nonsymmetric and symmetric potential wells are dealt with. This is applicable for large wavelengths compared with characteristic lengths of potential changes. In Appendices we represent the corresponding foundations of Generalized functions and apply them to barriers and wells and to transition functions. The Sturm-Liouville equation is not only interesting because some important second-order differential equations can be reduced to it but also because it is easier to demonstrates some details of the derivations for this one-dimensional equation than for the full three-dimensional vectorial equations of electrodynamics of media. The article continues a paper that was made long ago.

关键词： Schrödinger Equation Drude Approximation Transition Layer Potential Barrier Potential Well Reflection Refraction Moment Series Generalized Functions Delta Function and Its Derivatives Discrete or Bound Eigenstates

Innate immune responses induced by lipopolysaccharide and lipoteichoic acid in primary goat mammary epithelial cells

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Journal of Animal Science and Biotechnology 2017年第4期8卷 842-851页

作者： Omar Bulgari Xianwen Dong alfred.L.Roca1 Anna M. Caroli Juan J. Loor Department of Animal Sciences and Division of Nutritional Sciences University of Illinois at Urbana-Champaign Urbana IL 61801 USA Department of Molecular and Translational Medicine University of BresciaBrescia 25123 Italy Institute of Animal Nutrition Sichuan Agricultural University Chengdu 611130 China Division of Nutritional Sciences University of Illinois at Urbana-Champaign Urbana IL 61801 USA

Background: Innate immune responses induced by in vitro stimulation of primary mammary epithelial cells(MEC) using Gram-negative lipopolysaccharide(LPS) and Gram-positive lipoteichoic acid(LTA) bacterial cell wall components are well-characterized in bovine species. The objective of the current study was to characterize the downstream regulation of the inflammatory response induced by Toll-like receptors in primary goat MEC(pgMEC). We performed quantitative real-time RT-PCR(qPCR) to measure mRNA levels of 9 genes involved in transcriptional regulation or antibacterial activity: Toll-like receptor 2(TLR2), Toll-like receptor 4(TLR4), prostaglandin-endoperoxide synthase 2(PTGS2), interferon induced protein with tetratricopeptide repeats 3(IFIT3), interferon regulatory factor 3(IRF3), myeloid differentiation primary response 88(MYD88), nuclear factor of kappa light polypeptide gene enhancer in B-cells 1(NFKB1), Toll interacting protein(TOLLIP), and lactoferrin(LTF). Furthermore,we analyzed 7 cytokines involved in Toll-like receptor signaling pathways: C-C motif chemokine ligand 2(CCL2), C-C motif chemokine ligand 5(CCL5), C-X-C motif chemokine ligand 6(CXCL6), interleukin 8(CXCL8), interleukin 1 beta(IL1 B), interleukin 6(IL6), and tumor necrosis factor alpha(TNF).Results: Stimulation of pgMEC with LPS for 3 h led to an increase in expression of CCL2, CXCL6, IL6, CXCL8,PTGS2, IFIT3, MYD88, NFKB1, and TLR4(P < 0.05). Except for IL6, and PTGS2, the same genes had greater expression than controls at 6 h post-LPS(P < 0.05). Expression of CCL5, PTGS2, IFIT3, NFKB1, TLR4, and TOLLIP was greater than controls after 3 h of incubation with LTA(P < 0.05). Compared to controls, stimulation with LTA for 6 h led to greater expression of PTGS2, IFIT3, NFKB1, and TOLLIP(P < 0.05) whereas the expression of CXCL6, CXCL8, and TLR4 was lower(P < 0.05). At 3 h incubation with both toxins compared to controls a greater expression(P < 0.05) of CCL2, CCL5, CXCL6, CXCL8, IL6, PTGS2, IFIT3, IR

关键词： Gene expression Inflammation Lactation Mastitis

Convergence Phenomenon with Fourier Series of tg(x2)and Alike

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Advances in Pure Mathematics 2024年第7期14卷 556-595页

作者： alfred.Wünsche Institut fr Physik Humboldt-Universitt Berlin Berlin Germany

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

关键词： Gibbs Phenomenon Generalized Functions Weak Convergence Chebyshev Polynomials of First and Second Kind Even and Odd Generating Functions for Chebyshev Polynomials Polylogarithms Completeness Relations