The Riccati Equation in Mathematical Finance

AbstractThis paper uses ideas from symbolic computation to classify solutions to an important class of problems in mathematical finance and thus provides a linkage between these two fields. We show that Kovacic’s concept of closed-form solutions to the Riccati ordinary differential equation can be used to provide a precise mathematical definition that is useful in certain financial models. We extend this definition to a broader class of problems and discuss how these ideas can be usefully applied to practical problems in the finance area. We provide a specific application by developing a new implementation of the Cox–Ingersoll–Ross interest-rate model that may be of practical interest

On the physical contents of q-deformed Minkowski spaces

Some physical aspects of $q$-deformed spacetimes are discussed. It is pointed out that, under certain standard assumptions relating deformation and quantization, the classical limit (Poisson bracket description) of the dynamics is bound to contain unusual features. At the same time, it is argued that the formulation of an associated $q$-deformed field theory is fraught with serious difficulties.Comment: some changes mad

Patterns of carbon footprints of main grains production in China: a comparison between main and non-main producing areas

Understanding the spatiotemporal patterns of carbon footprints (CFs) of grains production is important to formulate regional heterogeneous greenhouse gas (GHG) mitigation strategies. This study evaluates the CFs, farm CFs (FCFs: CFs of per unit area), and production CFs (PCFs: CFs of per unit yield) of main grains production in China based on a new scale data set: agricultural statistics data of over 300 prefecture-level regions. A comparison of CFs of main grains production between main producing area (MPA) and non-main producing area (NMPA) are firstly discussed on a totally new scale. Results show that the CFs of main grains production of MPA accounts for 54-57% of country's total although the area of farmland of MPA only accounts for 42%. The PCF and FCF of rice production are higher in MPA, while those of wheat and maize production are lower in MPA. It implies that there are less GHG emission of rice (main paddy grain) productions in NMPA and less GHG emission of wheat and maize (main dryland grains) production in MPA. In additional, the PCF of rice shows growth, while that of wheat and maize shows decline from 2008 to 2017. The growth of PCF of rice is mainly driven by the rise of PCF in MPA. Findings are expected to improve the understanding patterns of China's CF of main grains production and subsequently contribute to GHG mitigation.Industrial Ecolog

Quantum and Classical Integrable Systems

The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the universal enveloping algebra of an affine Lie algebra, or its q-deformation.) A similar relation also holds in the classical case. We discuss different guises of this very important relation and its implication for the description of the spectrum and the eigenfunctions of the quantum system. Parallels between the classical and the quantum cases are thoroughly discussed.Comment: 59 pages, LaTeX2.09 with AMS symbols. Lectures at the CIMPA Winter School on Nonlinear Systems, Pondicherry, January 199

Identification of a novel distal regulatory element of the human Neuroglobin gene by the chromosome conformation capture approach

Neuroglobin (NGB) is predominantly expressed in the brain and retina. Studies suggest that NGB exerts protective effects to neuronal cells and is implicated in reducing the severity of stroke and Alzheimer's disease. However, little is known about the mechanisms which regulate the cell type-specific expression of the gene. In this study, we hypothesized that distal regulatory elements (DREs) are involved in optimal expression of the NGB gene. By chromosome conformation capture we identified two novel DREs located -70 kb upstream and +100 kb downstream from the NGB gene. ENCODE database showed the presence of DNaseI hypersensitive and transcription factors binding sites in these regions. Further analyses using luciferase reporters and chromatin immunoprecipitation suggested that the -70 kb region upstream of the NGB gene contained a neuronalspecific enhancer and GATA transcription factor binding sites. Knockdown of GATA-2 caused NGB expression to drop dramatically, indicating GATA-2 as an essential transcription factor for the activation of NGB expression. The crucial role of the DRE in NGB expression activation was further confirmed by the drop in NGB level after CRISPR-mediated deletion of the DRE. Taken together, we show that the NGB gene is regulated by a cell type-specific loop formed between its promoter and the novel DRE

Measurements of the Mass and Full-Width of the ηc\eta_c Meson

In a sample of 58 million $J/\psi$ events collected with the BES II detector, the process J/$\psi\to\gamma\eta_c$ is observed in five different decay channels: $\gamma K^+K^-\pi^+\pi^-$, $\gamma\pi^+\pi^-\pi^+\pi^-$, $\gamma K^\pm K^0_S \pi^\mp$ (with $K^0_S\to\pi^+\pi^-$), $\gamma \phi\phi$ (with $\phi\to K^+K^-$) and $\gamma p\bar{p}$. From a combined fit of all five channels, we determine the mass and full-width of $\eta_c$ to be $m_{\eta_c}=2977.5\pm1.0 ({stat.})\pm1.2 ({syst.})$ MeV/$c^2$ and $\Gamma_{\eta_c} = 17.0\pm3.7 ({stat.})\pm7.4 ({syst.})$ MeV/$c^2$.Comment: 9 pages, 2 figures and 4 table. Submitted to Phys. Lett.

Measurements of the observed cross sections for e+e−→e^+e^-\to exclusive light hadrons containing π0π0\pi^0\pi^0 at s=3.773\sqrt s= 3.773, 3.650 and 3.6648 GeV

By analyzing the data sets of 17.3, 6.5 and 1.0 pb$^{-1}$ taken, respectively, at $\sqrt s= 3.773$, 3.650 and 3.6648 GeV with the BES-II detector at the BEPC collider, we measure the observed cross sections for $e^+e^-\to \pi^+\pi^-\pi^0\pi^0$, $K^+K^-\pi^0\pi^0$, $2(\pi^+\pi^-\pi^0)$, $K^+K^-\pi^+\pi^-\pi^0\pi^0$ and $3(\pi^+\pi^-)\pi^0\pi^0$ at the three energy points. Based on these cross sections we set the upper limits on the observed cross sections and the branching fractions for $\psi(3770)$ decay into these final states at 90% C.L..Comment: 7 pages, 2 figure

Partial wave analysis of J/\psi \to \gamma \phi \phi

Using $5.8 \times 10^7 J/\psi$ events collected in the BESII detector, the radiative decay $J/\psi \to \gamma \phi \phi \to \gamma K^+ K^- K^0_S K^0_L$ is studied. The $\phi\phi$ invariant mass distribution exhibits a near-threshold enhancement that peaks around 2.24 GeV/$c^{2}$. A partial wave analysis shows that the structure is dominated by a $0^{-+}$ state ($\eta(2225)$) with a mass of $2.24^{+0.03}_{-0.02}{}^{+0.03}_{-0.02}$ GeV/$c^{2}$ and a width of $0.19 \pm 0.03^{+0.06}_{-0.04}$ GeV/$c^{2}$. The product branching fraction is: $Br(J/\psi \to \gamma \eta(2225))\cdot Br(\eta(2225)\to \phi\phi) = (4.4 \pm 0.4 \pm 0.8)\times 10^{-4}$.Comment: 11 pages, 4 figures. corrected proof for journa

Direct Measurements of Absolute Branching Fractions for D0 and D+ Inclusive Semimuonic Decays

By analyzing about 33 $\rm pb^{-1}$ data sample collected at and around 3.773 GeV with the BES-II detector at the BEPC collider, we directly measure the branching fractions for the neutral and charged $D$ inclusive semimuonic decays to be $BF(D^0 \to \mu^+ X) =(6.8\pm 1.5\pm 0.7)$ and $BF(D^+ \to \mu^+ X) =(17.6 \pm 2.7 \pm 1.8)$, and determine the ratio of the two branching fractions to be $\frac{BF(D^+ \to \mu^+ X)}{BF(D^0 \to \mu^+ X)}=2.59\pm 0.70 \pm 0.25$

Direct Measurements of the Branching Fractions for D0→K−e+νeD^0 \to K^-e^+\nu_e and D0→π−e+νeD^0 \to \pi^-e^+\nu_e and Determinations of the Form Factors f+K(0)f_{+}^{K}(0) and f+π(0)f^{\pi}_{+}(0)

The absolute branching fractions for the decays $D^0 \to K^-e ^+\nu_e$ and $D^0 \to \pi^-e^+\nu_e$ are determined using $7584\pm 198 \pm 341$ singly tagged $\bar D^0$ sample from the data collected around 3.773 GeV with the BES-II detector at the BEPC. In the system recoiling against the singly tagged $\bar D^0$ meson, $104.0\pm 10.9$ events for $D^0 \to K^-e ^+\nu_e$ and $9.0 \pm 3.6$ events for $D^0 \to \pi^-e^+\nu_e$ decays are observed. Those yield the absolute branching fractions to be $BF(D^0 \to K^-e^+\nu_e)=(3.82 \pm 0.40\pm 0.27)$ and $BF(D^0 \to \pi^-e^+\nu_e)=(0.33 \pm 0.13\pm 0.03)$. The vector form factors are determined to be $|f^K_+(0)| = 0.78 \pm 0.04 \pm 0.03$ and $|f^{\pi}_+(0)| = 0.73 \pm 0.14 \pm 0.06$. The ratio of the two form factors is measured to be $|f^{\pi}_+(0)/f^K_+(0)|= 0.93 \pm 0.19 \pm 0.07$.Comment: 6 pages, 5 figure