Investigation of experimental observables in search of the chiral magnetic effect in heavy-ion collisions in the STAR experiment

The chiral magnetic effect(CME)is a novel transport phenomenon,arising from the interplay between quantum anomalies and strong magnetic fields in chiral systems.In high-energy nuclear collisions,the CME may survive the expansion of the quark-gluon plasma fireball and be detected in experiments.Over the past two decades,experimental searches for the CME have attracted extensive interest at the Relativistic Heavy Ion Collider(RHIC)and the Large Hadron Collider(LHC).The main goal of this study is to investigate three pertinent experimental approaches:the$\gamma$correlator,the R correlator,and the signed balance functions.We exploit simple Monte Carlo simulations and a realistic event generator(EBE-AVFD)to verify the equivalence of the core components among these methods and to ascertain their sensitivities to the CME signal and the background contributions for the isobar collisions at the RHIC.     

Fast approximation of matroid packing and covering

We study packing problems with matroid structures, which includes the strength of a graph of Cunningham and scheduling problems. If \(\mathcal {M}\) is a matroid over a set of elements S with independent set \(\mathcal {I}\), and \(m=|S|\), we suppose that we are given an oracle function that takes an independent set \(A\in \mathcal {I}\) and an element \(e\in S\) and determines if \(A\cup \{e\}\) is independent in time I(m). Also, given that the elements of A are represented in an ordered way \(A=\{A_1,\dots ,A_k\}\), we denote the time to check if \(A\cup \{e\}\notin \mathcal {I}\) and if so, to find the minimum \(i\in \{0,\dots ,k\}\) such that \(\{A_1,\dots ,A_i\}\cup \{e\}\notin \mathcal {I}\) by \(I^*(m)\). Then, we describe a new FPTAS that computes for any \(\varepsilon >0\) and for any matroid \(\mathcal {M}\) of rank r over a set S of m elements, in memory space O(m), the packing \(\varLambda ({\mathcal {M}})\) within \(1+\varepsilon \) in time \(O(mI^*(m)\log (m)\log (m/r)/\varepsilon ^2)\), and the covering \(\varUpsilon ({\mathcal {M}})\) in time \(O(r\varUpsilon ({\mathcal {M}})I(m)\log (m)\log (m/r)/\varepsilon ^2)\). This method outperforms in time complexity by a factor of \(\varOmega (m/r)\) the FPTAS of Plotkin, Shmoys, and Tardos, and a factor of \(\varOmega (m)\) the FPTAS of Garg and Konemann. On top of the value of the packing and the covering, our algorithm exhibits a combinatorial object that proves the approximation. The applications of this result include graph partitioning, minimum cuts, VLSI computing, job scheduling and others.     

Continuous dependence on the boundary conditions for the Wentzell Laplacian

The solution u of the well-posed problem

AdS 5 Solutions of Type IIB Supergravity and Generalized Complex Geometry

We use the formalism of generalized geometry to study the generic supersymmetric AdS ₅ solutions of type IIB supergravity that are dual to ${\mathcal{N}=1}We use the formalism of generalized geometry to study the generic supersymmetric AdS ₅ solutions of type IIB supergravity that are dual to N=1{\mathcal{N}=1} superconformal field theories (SCFTs) in d = 4. Such solutions have an associated six-dimensional generalized complex cone geometry that is an extension of Calabi-Yau cone geometry. We identify generalized vector fields dual to the dilatation and R-symmetry of the dual SCFT and show that they are generalized holomorphic on the cone. We carry out a generalized reduction of the cone to a transverse four-dimensional space and show that this is also a generalized complex geometry, which is an extension of K?hler-Einstein geometry. Remarkably, provided the five-form flux is non-vanishing, the cone is symplectic. The symplectic structure can be used to obtain Duistermaat-Heckman type integrals for the central charge of the dual SCFT and the conformal dimensions of operators dual to BPS wrapped D3-branes. We illustrate these results using the Pilch-Warner solution.     

Stability estimates for nonlinear hyperbolic problems with nonlinear Wentzell boundary conditions

Of concern is the nonlinear hyperbolic problem with nonlinear dynamic boundary conditions $$\left\{ \begin{array}{lll} u_{tt} ={\rm div} (\mathcal{A} \nabla u)-\gamma (x,u_t), && \quad {\rm in} \; (0, \infty) \times \Omega,\\ u(0, \cdot)=f, \, u_t(0,\cdot)=g, && \quad {\rm in}\; \Omega, \\ u_{tt} + \beta \partial^ \mathcal{A}_\nu u+c(x)u+ \delta (x,u_t)-q \beta \Lambda_{\rm LB} u=0,&& \quad {\rm on} \;(0, \infty ) \times \partial \Omega . \end{array}\right. $$ for t ≥  0 and ${x \in \Omega \subset \mathbb{R}^N}$ ; the last equation holds on the boundary ?Ω. Here ${\mathcal{A}= \{a_{ij}(x)\}_{ij}}$ is a real, hermitian, uniformly positive definite N × N matrix; ${\beta \in C(\partial \Omega)}$ , with β > 0; ${\gamma:\Omega \times \mathbb{R} \to \mathbb{R}; \delta:\partial \Omega \times \mathbb{R} \to \mathbb{R}; \,c:\partial \Omega \to \mathbb{R}; \, q \ge 0, \Lambda_{\rm LB}}$ is the Laplace–Beltrami operator on ?Ω, and ${\partial^\mathcal{A}_\nu u}$ is the conormal derivative of u with respect to ${\mathcal{A}}$ ; everything is sufficiently regular. We prove explicit stability estimates of the solution u with respect to the coefficients ${\mathcal{A},\,\beta,\,\gamma,\,\delta,\,c,\,q}$ , and the initial conditions f, g. Our arguments cover the singular case of a problem with q = 0 which is approximated by problems with positive q.     

General and Practical Formation of Thiocyanates from Thiols

A new method for the cyanation of thiols and disulfides using cyanobenziodoxol(on)e hypervalent iodine reagents is described. Both aliphatic and aromatic thiocyanates can be accessed in good yields in a few minutes at room temperature starting from a broad range of thiols with high chemioselectivity. The complete conversion of disulfides to thiocyanates was also possible. Preliminary computational studies indicated a low energy concerted transition state for the cyanation of the thiolate anion or radical. The developed thiocyanate synthesis has broad potential for various applications in synthetic chemistry, chemical biology and materials science.