A new convolution theorem associated with the linear canonical transform

In this paper, we first introduce a new notion of canonical convolution operator, and show that it satisfies the commutative, associative, and distributive properties, which may be quite useful in signal processing. Moreover, it is proved that the generalized convolution theorem and generalized Young's inequality are also hold for the new canonical convolution operator associated with the LCT. Finally, we investigate the sufficient and necessary conditions for solving a class of convolution equations associated with the LCT.Comment: 13 page

M-Theory Brane as Giant Graviton and the Fractional Quantum Hall Effect

A small number of M-theory branes as giant gravitons in the M-theory sector of LLM geometry is studied as a probe. The abelian way shows that the low energy effective action for M-theory brane is exactly the 2d electron subject to a vertical magnetic field. We also briefly discuss the microscopic description of M2-brane giant graviton in this geometry, in the language of a combination of D0-branes as fuzzy 2-spheres. Then we go to the well-established Noncommutative Chern-Simons theory description. After quantization, well behaved Fractional Quantum Hall Effect is demonstrated. This goes beyond the original LLM description and should be some indication of novel geometry.Comment: 20 pages, uses JHEP3.cl

Bidirectional and passive optical field to microwave field quantum converter with high bandwidth

The conversion between microwave photons and optical photons with quantum coherence is important for quantum communication and computation. In this paper, we report a proposal using an ensemble of atoms coupled to microwave and optical resonators. Input photons to one resonator are converted into output photons in the other resonator without active operation. Usually the conversion is only optimized at certain frequency. In our proposal, we find that the efficiency is almost a constant and can be close to 100% in a large interval of frequency, i.e. a high-bandwidth conversion can be realized with our proposal.Comment: 6 pages, 4 figure

Effective Field Theory of Integrating out Sfermions in the MSSM: Complete One-Loop Analysis

We apply the covariant derivative expansion of the Coleman-Weinberg potential to the sfermion sector in the minimal supersymmetric standard model, matching it to the relevant dimension-6 operators in the standard model effective field theory at one-loop level. Emphasis is paid to nondegenerate large soft supersymmetry breaking mass squares, and the most general analytical Wilson coefficients are obtained for all pure bosonic dimension-6 operators. In addition to the non-logarithmic contributions, they generally have another logarithmic contributions. Various numerical results are shown, in particular the constraints in the large $X_t$ branch reproducing the $125$~GeV Higgs mass can be pushed to high values to almost completely probe the low stop mass region at the future FCC-ee experiment, even given the Higgs mass calculation uncertainty.Comment: Correction of Wilson coefficients to match 1512.03003, numerically constraints almost unchanged, published versio

A mathematical model about human infections of H7N9 influenza in China with the intervention of live poultry markets closing

This paper develops a deterministic differential equations model that captures the H7N9 virus transmission from live poultry to human via poultry-human contacts in live poultry markets (LPMs). The virus circulation among live poultry, which happens but is hard to be detected (since contaminated live poultry appear to be asymptomatic), is also incorporated in the model. The time-dependent contact rate between human and live poultry based on LPMs closing information can be estimated. From data of LPMs closing news, the contact rate function can be easily estimated. This model could serve as a rational basis for public health authorities to evaluate the effectiveness of LPM closing, as well as other interventions according to simple modifications. Without data about daily cases, I also provide suggestions for some of the basic parameters that would be a useful fitness parameter set for future simulation

LpL^p estimates for the Bergman projection on some Reinhardt domains

We obtain $L^p$ regularity for the Bergman projection on some Reinhardt domains. We start with a bounded initial domain $\Omega$ with some symmetry properties and generate successor domains in higher {dimensions}. We prove: If the Bergman kernel on $\Omega$ satisfies appropriate estimates, then the Bergman projection on the successor is $L^p$ bounded. For example, the Bergman projection on successors of strictly pseudoconvex initial domains is bounded on $L^p$ for $1<p<\infty$. The successor domains need not have smooth boundary nor be strictly pseudoconvex.Comment: 12 pages, accepted for publication in Proceedings of AM

Refracting into Ultra Diffuse Galaxy NGC 1052-DF2 by Passing near the Center of NGC 1052

The recent observation of the ultra-diffuse galaxy NGC 1052-DF2 shows a galaxy may lack dark matter. Usually dark matter is much more abundant than stellar in galaxy environment. This dark matter to baryon mass ratio is generally larger than the cosmological ratio of about five, since a significant part of baryon is diffused in the form of intergalactic medium. How to achieve such a low dark matter to baryon mass ratio is a challenge to the standard galaxy formation mechanism. Here we show that such a low ratio can be a natural consequence if the NGC 1052-DF2 had experienced a single passage within a few kpcs to the center of galaxy NGC 1052. The tidal effect of NGC 1052 in the encounter will heat the NGC 1052-DF2 up, stretch the previous dwarf galaxy significantly into its current size. The relative lacking of dark matter in the observed region is a natural consequence of the dark matter extended distribution and relatively less concentration in the corresponding central region before encounter, together with a systematic underestimation of the trace mass estimator method during relaxation after encounter. The observed flat distribution of the ultra-diffuse galaxy can be reproduced. Our results shows no need of introducing any new physical mechanism.Comment: 6 pages, 4 figure

The Bergman Kernel on some Hartogs domains

We obtain new explicit formulas for the Bergman kernel function on two families of Hartogs domains. To do so, we first compute the Bergman kernels on the slices of these Hartogs domains with some coordinates fixed, evaluate these kernel functions at certain points off the diagonal, and then apply a first order differential operator to them. We find, for example, explicit formulas for the kernel function on $$\{(z_1,z_2,w)\in\mathbb C^3:e^{|w|^2}|z_1|^2+|z_2|^2<1\}$$ and on $$\{(z_1,z_2,w)\in\mathbb C^3:|z_1|^2+|z_2|^2+|w|^2<1+|z_2w|^2\;{\rm and} \;|w|<1\}.$$ We use our formulas to determine the boundary behavior of the kernel function of these domains on the diagonal.Comment: 24 pages, accepted for publication in The Journal of Geometric Analysi

Modeling of Contact Tracing in Epidemic Populations Structured by Disease Age

We consider an age-structured epidemic model with two basic public health interventions: (i) identifying and isolating symptomatic cases, and (ii) tracing and quarantine of the contacts of identified infectives. The dynamics of the infected population are modeled by a nonlinear infection-age-dependent partial differential equation, which is coupled with an ordinary differential equation that describes the dynamics of the susceptible population. Theoretical results about global existence and uniqueness of positive solutions are proved. We also present two practical applications of our model: (1) we assess public health guidelines about emergency preparedness and response in the event of a smallpox bioterrorist attack; (2) we simulate the 2003 SARS outbreak in Taiwan and estimate the number of cases avoided by contact tracing. Our model can be applied as a rational basis for decision makers to guide interventions and deploy public health resources in future epidemics

Time irreversibility in the quantum systems with infinite number of particles

The time irreversible evolution of quantum systems with infinite number of particles (QSINP) was studied within a newly constructed algebraic framework. The QSINP could be described by the quantum infinite lattice field. The *-Algebra R is the set of all dynamic variables of the QSINP, in which a special addition and multiplication operations were defined. The full pure state vector (FPSV) \rho, the pure state vector {\rho_f} and the equivalent relations within them are also well defined. The set of all pure state vectors, which are equivalent to the FPSV \rho, is a Hilbert Space {H_\rho}, if the addition, the inner product and the norm were defined in it. The set of all linear transformation {N_\rho} on {H_\rho} is isomorphic to R, and {{N_\rho},{H_\rho}} is the representation of R, associated with \rho. The *-Algebra R has infinitely many non-equivalent irreducible GNS constructions (representations), associated with different nonequivalent FPSVs respectively. It is proved that, the dynamical motions of the QSINP is totally within the GNS construction associated with the initial pure state vector; However, the time reversal transformation makes the initial FPSV and its corresponding dynamical evolution into another non-equivalent GNS construction. Therefore, within the GNS construction associated with the FPSV, the dynamics of the QSINP is time irreversible. Finally, due to the Liouville operator has real continuous spectrum within the GNS construction, the longtime asymptotic solution of Liouville equation in the GNS construction could be treated by the formal scattering theory. The Master equation with dissipative term was obtained, which is formally irrelevant of the initial state and the corresponding GNS construction. This master equation could be regarded as the evolution equation of the QSINP on R