Searching for cosmological preferred axis using cosmographic approach

Recent released Planck data and other astronomical observations show that the universe may be anisotropic on large scales. This hints a cosmological privileged axis in our anisotropic expanding universe. This paper proceeds a modified redshift in anisotropic cosmological model as \( 1+\tilde{z}(t,\hat{\mathbf{p }})=\frac{a(t_{0)}}{a(t)}(1-A(\hat{\mathbf{n }}.\hat{\mathbf{p }}))\) (where A is the magnitude of anisotropy, \(\hat{\mathbf{n }}\) is the direction of privileged axis, and \(\hat{\mathbf{p }}\) is the direction of each SNe Ia sample to galactic coordinates) along with anisotropic parameter \(\delta =\frac{A(\hat{\mathbf{n }}.\hat{\mathbf{p }})}{1+A(\hat{\mathbf{n }}.\hat{\mathbf{p }})}\). The luminosity distance is expanded with model-independent cosmographic parameters as a function of modified redshift \(\tilde{z}\). As the transformation matrix \(M(n\times n)\) is obtained to convert the Taylor series coefficients of isotropic luminosity distance to corresponding anisotropic parameters. These results culminate the magnitude of anisotropy about \(\mid A\mid \simeq 10^{-3}\) and the direction of preferred axis as \((l,b)=\left( 297^{-34}_{+34},3^{-28}_{+28}\right) \), which are consistent with other studies in \(1-\sigma \) confidence level.     

Quantum Fisher Information for <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(2) Atomic Coherent States and <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(1, 1) Coherent States

We investigate quantum Fisher information (QFI) for s u(2) atomic coherent states and s u(1, 1) coherent states. In this work, we find that for s u(2) atomic coherent states, the QFI with respect to \(\vartheta ~(\mathcal {F}_{\vartheta })\) is independent of φ, the QFI with respect to \(\varphi (\mathcal {F}_{\varphi })\) is governed by ??. Analogously, for s u(1,1) coherent states, \(\mathcal {F}_{\tau }\) is independent of φ, and \(\mathcal {F}_{\varphi }\) is determined by τ. Particularly, our results show that \(\mathcal {F}_{\varphi }\) is symmetric with respect to ?? = π/2 for s u(2) atomic coherent states. And for s u(1,1) coherent states, \(\mathcal {F}_{\varphi }\) also possesses symmetry with respect to τ = 0.     

Degeneration of Bethe subalgebras in the Yangian of $$\mathfrak {gl}_n$$

We study degenerations of Bethe subalgebras B(C) in the Yangian \(Y(\mathfrak {gl}_n)\), where C is a regular diagonal matrix. We show that closure of the parameter space of the family of Bethe subalgebras, which parameterizes all possible degenerations, is the Deligne–Mumford moduli space of stable rational curves \(\overline{M_{0,n+2}}\). All subalgebras corresponding to the points of \(\overline{M_{0,n+2}}\) are free and maximal commutative. We describe explicitly the “simplest” degenerations and show that every degeneration is the composition of the simplest ones. The Deligne–Mumford space \(\overline{M_{0,n+2}}\) generalizes to other root systems as some De Concini–Procesi resolution of some toric variety. We state a conjecture generalizing our results to Bethe subalgebras in the Yangian of arbitrary simple Lie algebra in terms of this De Concini–Procesi resolution.     

Parabolic Presentations of the Super Yangian {Y(\mathfrak{gl}_{M|N})} Associated with Arbitrary 01-Sequences

Let μ be an arbitrary composition of M + N and let \({\mathfrak{s}}\) be an arbitrary \({0^{M}1^{N}}\)- sequence. A new presentation, depending on \({\mu \rm and \mathfrak{s}}\), of the super Yangian Y_M|N associated to the general linear Lie superalgebra \({\mathfrak{gl}_{M|N}}\) is obtained.     

A new decay mode of higher charmonium

We calculate the \(\Lambda _c{\bar{\Lambda }}_c\) partial decay width of the excited vector charmonium states around 4.6 GeV with the quark pair creation model. We find that the partial decay width of the \(\Lambda _c{\bar{\Lambda }}_c\) mode can reach up to several MeV for \(\psi (4S,~5S,~6S)\). In contrast, the partial \(\Lambda _c{\bar{\Lambda }}_c\) decay width of the states \(\psi (3D,~4D,~5D)\) is less than one MeV. If the enhancement Y(4630) reported by the Belle Collaboration in \(\Lambda _c{\bar{\Lambda }}_c\) invariant-mass distribution is the same structure as Y(4660), the Y(4660) resonance is most likely to be a S-wave charmonium state.     

Synthesis,characterization and molecular docking studies of thiouracil derivatives as potent thymidylate synthase inhibitors and potential anticancer agents

Thymidylate synthase (TS), one of folate-dependent enzymes, is a key and well-recognized target for anticancer agents. In this study, a series of 6-aryl-5-cyano thiouracil derivatives were designed and synthesized in accordance with essential pharmacophoric features of known TS inhibitors. Nineteen compounds were screened in vitro for their anti-proliferative activities toward HePG-2, MCF-7, HCT-116, and PC-3 cell lines. Compounds \(\mathbf{21}_{\mathbf{c}}\), \(\mathbf{21}_{\mathbf{d}}\), and 24 exhibited high anti-proliferative activity, comparable to that of 5-fluorouracil. Additionally, ten compounds with potent anti-proliferative activities were further evaluated for their ability to inhibit TS enzyme. Six compounds (\(\mathbf{21}_{\mathbf{b}}\), \(\mathbf{21}_{\mathbf{c}}\), \(\mathbf{21}_{\mathbf{d}}\), 22, 23 and 24) demonstrated potent dose-related TS inhibition with \(\hbox {IC}_{50}\) values ranging from 1.57 to \(3.89\,\upmu \hbox {M}\). The in vitro TS activity results were consistent with those of the cytotoxicity assay where the most potent anti-proliferative compounds of the series showed good TS inhibitory activity comparable to that of 5-fluorouracil. Furthermore, molecular docking studies were carried out to investigate the binding pattern of the designed compounds with the prospective target, TS (PDB-code: 1JU6).     

The strong decays of <Emphasis Type="Italic">X</Emphasis>(3940) and <Emphasis Type="Italic">X</Emphasis>(4160)

The new mesons X(3940) and X(4160) have been found by Belle Collaboration in the processes \(e^+e^-\rightarrow J/\psi D^{(*)}{\bar{D}}^{(*)}\). Considering X(3940) and X(4160) as \(\eta _c(3S)\) and \(\eta _c(4S)\) states, the two-body open charm OZI-allowed strong decay of \(\eta _c(3S)\) and \(\eta _c(4S)\) are studied by the improved Bethe–Salpeter method combined with the \(^3P_0\) model. The strong decay width of \(\eta _c(3S)\) is \(\Gamma _{\eta _c(3S)}=(33.5^{+18.4}_{-15.3})\) MeV, which is close to the result of X(3940); therefore, \(\eta _c(3S)\) is a good candidate of X(3940). The strong decay width of \(\eta _c(4S)\) is \(\Gamma _{\eta _c(4S)}=(69.9^{+22.4}_{-21.1})\) MeV, considering the errors of the results, it is close to the lower limit of X(4160). But the ratio of the decay width \(\frac{\Gamma (D{\bar{D}}^*)}{\Gamma (D^*{\bar{D}}^*)}\) of \(\eta _c(4S)\) is larger than the experimental data of X(4160). According to the above analysis, \(\eta _c(4S)\) is not the candidate of X(4160), and more investigations of X(4160) is needed.     

Dynamical generation of flavour

We propose the generation of Standard Model fermion hierarchy by the extension of renormalizable SO(10) GUT with O(N_g) family gauge symmetry. In this scenario, Higgs representations of SO(10) also carry family indices and are called Yukawons. Vacuum expectation values of these Yukawon fields break GUT and family symmetry and generate MSSM Yukawa couplings dynamically. We have demonstrated this idea using \({\mathbf {10}}\oplus {\mathbf {210}} \oplus {\mathbf {126}} \oplus {\overline {\mathbf {126}}}\) Higgs irrep, ignoring the contribution of 120-plet which is, however, required for complete fitting of fermion mass-mixing data. The effective MSSM matter fermion couplings to the light Higgs pair are determined by the null eigenvectors of the MSSM-type Higgs doublet superfield mass matrix \(\mathcal {H}\). A consistency condition on the doublet ([1,2,±1]) mass matrix (\(\text {Det}(\mathcal {H})=\) 0) is required to keep one pair of Higgs doublets light in the effective MSSM. We show that the Yukawa structure generated by null eigenvectors of \(\mathcal {H}\) are of generic kind required by the MSSM. A hidden sector with a pair of (S_ab; ?_ab) fields breaks supersymmetry and facilitates \(D_{O(N_{g})}\hspace *{-1pt}=\) 0. SUSY breaking is communicated via supergravity. In this scenario, matter fermion Yukawa couplings are reduced from 15 to just 3 parameters in MSGUT with three generations.     

Braidings of Tensor Spaces

Let V be a braided vector space, i.e., a vector space together with a solution \({\hat{R}\in {{End}}(V\otimes V)}\) of the Yang–Baxter equation. Denote \({T(V):=\bigoplus_k V^{\otimes k}}\) . We associate to \({\hat{R}}\) a one-parameter family of solutions \({T(\hat{R})\in {\rm End}(T(V)\otimes T(V))}\) of the Yang–Baxter equation on the tensor space T (V). Main ingredients of the solution are braid analogues of the binomial coefficients and of the Pochhammer symbols. The association \({\hat{R}\rightsquigarrow T(\hat{R})}\) is functorial with respect to V.     

Domain and Range of the Modified Wave Operator for Schrödinger Equations with a Critical Nonlinearity

We study the final problem for the nonlinear Schrödinger equation

$i{\partial }_{t}u+\frac{1}{2}\Delta u=\lambda|u|^{\frac{2}{n}}u,\quad (t,x)\in {\mathbf{R}}\times \mathbf{R}^{n},$

where\(\lambda \in{\bf R},n=1,2,3\). If the final data\(u_{+}\in {\bf H}^{0,\alpha }=\left\{ \phi \in {\bf L}^{2}:\left( 1+\left\vert x\right\vert \right) ^{\alpha }\phi \in {\bf L}^{2}\right\} \) with\(\frac{ n}{2} < \alpha < \min \left( n,2,1+\frac{2}{n}\right) \) and the norm\(\Vert \widehat{u_{+}}\Vert _{{\bf L}^{\infty }}\) is sufficiently small, then we prove the existence of the wave operator in L ². We also construct the modified scattering operator from H ^0,α to H ^0,δ with\(\frac{n}{2} < \delta < \alpha\).

     

Scaling exponents of forced polymer translocation through a nanopore

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (Nof the average translocation time \(\ensuremath \langle\tau\rangle\) , the average velocity of the center of mass \(\ensuremath \langle v_{{\rm CM}}\rangle\) , and the effective radius of gyration \(\ensuremath \langle {R}_g\rangle\) during the translocation process defined as \(\ensuremath \langle\tau\rangle \sim N^{\alpha}\) , \(\ensuremath \langle v_{{\rm CM}} \rangle \sim N^{-\delta}\) , and \(\ensuremath {R}_g \sim N^{\bar{\nu}}\) respectively, and the exponent of the translocation coordinate (s -coordinate) as a function of the translocation time \(\ensuremath \langle s^2(t)\rangle\sim t^{\beta}\) . We find \(\ensuremath \alpha=1.36 \pm 0.01\) , \(\ensuremath \beta=1.60 \pm 0.01\) for \(\ensuremath \langle s^2(t)\rangle\sim \tau^{\beta}\) and \(\ensuremath \bar{\beta}=1.44 \pm 0.02\) for \(\ensuremath \langle\Delta s^2(t)\rangle\sim\tau^{\bar{\beta}}\) , \(\ensuremath \delta=0.81 \pm 0.04\) , and \(\ensuremath \bar{\nu}\simeq\nu=0.59 \pm 0.01\) , where \( \nu\) is the equilibrium Flory exponent in 3D. Therefore, we find that \(\ensuremath \langle\tau\rangle\sim N^{1.36}\) is consistent with the estimate of \(\ensuremath \langle\tau\rangle\sim\langle R_g \rangle/\langle v_{{\rm CM}} \rangle\) . However, as observed previously in Monte Carlo (MC) calculations by Kantor and Kardar (Y. Kantor, M. Kardar, Phys. Rev. E 69, 021806 (2004)) we also find the exponent α = 1.36 ± 0.01 < 1 + ν. Further, we find that the parallel and perpendicular components of the gyration radii, where one considers the “cis” and “trans” parts of the chain separately, exhibit distinct out-of-equilibrium effects. We also discuss the dependence of the effective exponents on the pore geometry for the range of N studied here.     

Recent results on kaon decays by the NA48/2 experiment at CERN

The NA48/2 experiment reports the first observation of the rare decay K^± → π^±π⁰e⁺e^?, based on about 2000 candidates from 2003 data. The preliminary branching ratio in the full kinematic region is \(\mathcal {B}(K^{\pm } \to \pi ^{\pm }\pi ^{0}e^{+}e^{-})=(4.06\pm 0.17)\cdot 10^{-6}\). A sample of 4.687 × 10⁶\(K^{\pm }\to \pi ^{\pm }{\pi ^{0}_{D}}\) events collected in 2003/4 is analyzed to search for the dark photon (\(A^{\prime }\)) via the decay chain K^± → π^±π⁰, \(\pi ^{0}\to \gamma A^{\prime }\), \(A^{\prime }\to e^{+}e^{-}\). No signal is observed, limits in the plane mixing parameter ε² versus its mass \(m_{A^{\prime }}\) are reported.     

Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M(x) of a research object is defined by the researcher–modeler as a space¹ (X, p(X), \(P{I^{\bar x}}\), \(Be{l^{\bar x}}\)) with plausibility\(P{I^{\bar x}}\) and believability \(Be{l^{\bar x}}\) measures, where x is an uncertain element taking values in X that models researcher—modeler’s uncertain propositions about an unknown x ∈ X, measures \(P{I^{\bar x}}\), \(Be{l^{\bar x}}\) model modalities of a researcher–modeler’s subjective judgments on the validity of each x ∈ X: the value of \(P{I^{\bar x}}(\tilde x = x)\) determines how relatively plausible, in his opinion, the equality \((\tilde x = x)\) is, while the value of \(Be{l^{\bar x}}(\tilde x = x)\) determines how the inequality \((\tilde x = x)\) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher–modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike “standard” mathematical modeling, ?enables a researcher–modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model \(M(\tilde x)\), and if the data on observations of a research object is available, then it: ?enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research object.     

Non-Negative Integral Level Affine Lie Algebra Tensor Categories and Their Associativity Isomorphisms

For a finite-dimensional simple Lie algebra \({\mathfrak{g}}\), we use the vertex tensor category theory of Huang and Lepowsky to identify the category of standard modules for the affine Lie algebra \({{\widehat{\mathfrak{g}}}}\) at a fixed level \({\ell\in\mathbb{N}}\) with a certain tensor category of finite-dimensional \({\mathfrak{g}}\)-modules. More precisely, the category of level ? standard \({{\widehat{\mathfrak{g}}}}\)-modules is the module category for the simple vertex operator algebra \({L_{\widehat{\mathfrak{g}}}(\ell, 0)}\), and as is well known, this category is equivalent as an abelian category to \({\mathbf{D}(\mathfrak{g},\ell)}\), the category of finite-dimensional modules for the Zhu’s algebra \({A{(L_{\widehat{\mathfrak{g}}}(\ell, 0))}}\), which is a quotient of \({U(\mathfrak{g})}\). Our main result is a direct construction using Knizhnik–Zamolodchikov equations of the associativity isomorphisms in \({\mathbf{D}(\mathfrak{g},\ell)}\) induced from the associativity isomorphisms constructed by Huang and Lepowsky in \({{L_{\widehat{\mathfrak{g}}}(\ell, 0) - \mathbf{mod}}}\). This construction shows that \({\mathbf{D}(\mathfrak{g},\ell)}\) is closely related to the Drinfeld category of \({U(\mathfrak{g})}\)[[h]]-modules used by Kazhdan and Lusztig to identify categories of \({{\widehat{\mathfrak{g}}}}\)-modules at irrational and most negative rational levels with categories of quantum group modules.     

Two Phases of the Non-Commutative Quantum Mechanics with the Generalized Uncertainty Relations

We consider the quantum mechanics on the noncommutative plane with the generalized uncertainty relations \({\Delta } x_{1} {\Delta } x_{2} \ge \frac {\theta }{2}, {\Delta } p_{1} {\Delta } p_{2} \ge \frac {\bar {\theta }}{2}, {\Delta } x_{i} {\Delta } p_{i} \ge \frac {\hbar }{2}, {\Delta } x_{1} {\Delta } p_{2} \ge \frac {\eta }{2}\). We show that the model has two essentially different phases which is determined by \(\kappa = 1 + \frac {1}{\hbar ^{2} } (\eta ^{2} - \theta \bar {\theta })\). We construct a operator \(\hat {\pi }_{i}\) commuting with \(\hat {x}_{j} \) and discuss the harmonic oscillator model in two dimensional non-commutative space for three case κ > 0, κ = 0, κ < 0. Finally, we discuss the thermodynamics of a particle whose hamiltonian is related to the harmonic oscillator model in two dimensional non-commutative space.     

Phenomenology of light- and strange-quark simultaneous production at high energies

This letter presents an extension of EPL116(2017)62001 to light- and strange-quark nonequilibrium chemical phase-space occupancy factors (γ_q,s). The resulting damped trigonometric functionalities relating γ_q,s to the nucleon-nucleon center-of-mass energies (\(\sqrt {{s_{NN}}} \)) looks very similar except different coefficients. The phenomenology of the resulting γ_q,s(\(\sqrt {{s_{NN}}} \)) describes a rapid decrease at \(\sqrt {{s_{NN}}} \) ? 7GeV followed by a faster increase up to ~20 GeV. Then, both γ_q,s become nonsensitive to \(\sqrt {{s_{NN}}} \). Although these differ from γ _s (\(\sqrt {{s_{NN}}} \))obtained at γ _q (\(\sqrt {{s_{NN}}} \))=1, various particle ratios including K⁺/π⁺, K^?/π^?, Λ/π^?, Λ?/π^?, Ξ⁺/π⁺, and Ω/π^?, can well be reproduced, as well. We conclude that γ_q,s(\(\sqrt {{s_{NN}}} \)) should be instead determined from fits of various particle yields and ratios but not merely from fits to the particle ratio K⁺/π⁺.     

Regularity of the Speed of Biased Random Walk in a One-Dimensional Percolation Model

We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. Axelson-Fisk and Häggström established for this model a phase transition for the asymptotic linear speed \(\overline{\hbox {v}}\) of the walk. Namely, there exists some critical value \(\lambda _{\hbox {c}}>0\) such that \(\overline{\hbox {v}}>0\) if \(\lambda \in (0,\lambda _{\hbox {c}})\) and \(\overline{\hbox {v}}=0\) if \(\lambda \ge \lambda _{\hbox {c}}\). We show that the speed \(\overline{\hbox {v}}\) is continuous in \(\lambda \) on \((0,\infty )\) and differentiable on \((0,\lambda _{\hbox {c}}/2)\). Moreover, we characterize the derivative as a covariance. For the proof of the differentiability of \(\overline{\hbox {v}}\) on \((0,\lambda _{\hbox {c}}/2)\), we require and prove a central limit theorem for the biased random walk. Additionally, we prove that the central limit theorem fails to hold for \(\lambda \ge \lambda _{\hbox {c}}/2\).     

Asymptotic Behavior of the Selberg Zeta Functions for Degenerating Families of Hyperbolic Manifolds

Let {M _k } be a degenerating sequence of finite volume, hyperbolic manifolds of dimension d, with d = 2 or d = 3, with finite volume limit M _∞. Let \({Z_{M_{k}} (s)}\) be the associated sequence of Selberg zeta functions, and let \({{\mathcal{Z}}_{k} (s)}\) be the product of local factors in the Euler product expansion of \({Z_{M_{k}} (s)}\) corresponding to the pinching geodesics on M _k . The main result in this article is to prove that \({Z_{M_{k}} (s)/{\mathcal{Z}}_{k} (s)}\) converges to \({Z_{M_{\infty}} (s)}\) for all \({s \in \mathbf{C}}\)with Re(s) > (d ? 1)/2. The significant feature of our analysis is that the convergence of \({Z_{M_{k}} (s)/{\mathcal{Z}}_{k} (s)}\) to \({Z_{M_{\infty}} (s)}\) is obtained up to the critical line, including the right half of the critical strip, a region where the Euler product definition of the Selberg zeta function does not converge. In the case d = 2, our result reproves by different means the main theorem in Schulze (J Funct Anal 236:120–160, 2006).     

On a Classical Limit of <Emphasis Type="Italic">q</Emphasis>-Deformed Whittaker Functions

Previously, we derive a representation of q-deformed \({\mathfrak{gl}_{\ell+1}}\) -Whittaker function as a sum over Gelfand–Zetlin patterns. This representation provides an analog of the Shintani–Casselman–Shalika formula for q-deformed \({\mathfrak{gl}_{\ell+1}}\) -Whittaker functions. In this note, we provide a derivation of the Givental integral representation of the classical \({\mathfrak{gl}_{\ell+1}}\) -Whittaker function as a limit q → 1 of the sum over the Gelfand–Zetlin patterns representation of the q-deformed \({\mathfrak{gl}_{\ell+1}}\) -Whittaker function. Thus, Givental representation provides an analog the Shintani–Casselman–Shalika formula for classical Whittaker functions.