The Chern Coefficient and Cohen-Macaulay rings

The purpose of this paper is to investigate a relationship between the index of reducibility and the Chern coefficient for primary ideals. Therefore, the main result of this paper gives a characterization of a Cohen-Macaulay ring in terms of its the index of reducibility, its Cohen-Macaulay type, and the Chern coefficient for parameter ideals. As corollaries to the main theorem we obtained the characterizations of a Gorenstein ring in term of its Chern coefficient for parameter ideals

A Self-Consistent Model for the Formation of Relativistic Outflows in Advection-Dominated Accretion Disks with Shocks

In this Letter, we suggest that the relativistic protons powering the outflows emanating from radio-loud systems containing black holes are accelerated at standing, centrifugally-supported shocks in hot, advection-dominated accretion disks. Such disks are ideal sites for first-order Fermi acceleration at shocks because the gas is tenuous, and consequently the mean free path for particle-particle collisions generally exceeds the thickness of the disk. The accelerated particles are therefore able to avoid thermalization, and as a result a small fraction of them achieve very high energies and escape from the disk. In our approach the hydrodynamics and the particle acceleration are coupled and the solutions are obtained self-consistently based on a rigorous mathematical treatment. The theoretical analysis of the particle transport parallels the early studies of cosmic-ray acceleration in supernova shock waves. We find that particle acceleration in the vicinity of the shock can extract enough energy to power a relativistic jet. Using physical parameters appropriate for M87 and Sgr A*, we confirm that the jet kinetic luminosities predicted by the theory agree with the observational estimates.Comment: accepted for publication in Astrophysical Journal Letter

Hilbert functions of socle ideals

In this paper, we explore a relationship between Hilbert functions and the irreducible decompositions of ideals in local rings. Applications are given to characterize the regularity, Gorensteinness, Cohen-Macaulayness and sequentially Cohen-Macaulayness of local rings.Comment: arXiv admin note: substantial text overlap with arXiv:1504.0604

Face Alignment Using Active Shape Model And Support Vector Machine

The Active Shape Model (ASM) is one of the most popular local texture models for face alignment. It applies in many fields such as locating facial features in the image, face synthesis, etc. However, the experimental results show that the accuracy of the classical ASM for some applications is not high. This paper suggests some improvements on the classical ASM to increase the performance of the model in the application: face alignment. Four of our major improvements include: i) building a model combining Sobel filter and the 2-D profile in searching face in image; ii) applying Canny algorithm for the enhancement edge on image; iii) Support Vector Machine (SVM) is used to classify landmarks on face, in order to determine exactly location of these landmarks support for ASM; iv)automatically adjust 2-D profile in the multi-level model based on the size of the input image. The experimental results on Caltech face database and Technical University of Denmark database (imm_face) show that our proposed improvement leads to far better performance.Comment: 11 pages and 11 figure

Jet Launching Radius in Low-Power Radio-Loud AGNs in Advection-Dominated Accretion Flows

Using our theory for the production of relativistic outflows, we estimate the jet launching radius and the inferred mass accretion rate for 52 low-power radio-loud AGNs based on the observed jet powers. Our analysis indicates that (1) a significant fraction of the accreted energy is required to convert the accreted mass to relativistic energy particles for the production of the jets near the event horizon, (2) the jets launching radius moves radially toward the horizon as the mass accretion rate or jets power increases, and (3) no jet/outflow formation is possible beyond 44 gravitational radii.Comment: 16 pages, 9 figures, 3 tables, accepted by MNRAS (Mar. 09, 2018); v2: references update

Asymptotic Behaviour of Parameter Ideals in Generalized Cohen-Macaulay Modules

The purpose of this paper is to give affirmative answers to two open questions as follows. Let (R, \m) be a generalized Cohen-Macaulay Noetherian local ring. Both questions, the first question was raised by M. Rogers \cite {R} and the second one is due to S. Goto and H. Sakurai \cite {GS1}, ask whether for every parameter ideal \q contained in a high enough power of the maximal ideal \m the following statements are true: (1) The index of reducibility N_R(\q;R) is independent of the choice of \q; and (2) I^2=\q I, where I=\q:_R\m.Comment: 12 page

Parametric Decomposition of Powers of Parameter Ideals and Sequentially Cohen-Macaulay Modules

Let $M$ be a finitely generated module of dimension $d$ over a Noetherian local ring (R,\m) and \q the parameter ideal generated by a system of parameters \x = (x_1,..., x_d) of $M$. For each positive integer $n$, set $$\Lambda_{d,n}=\{\alpha =(\alpha_1,...,\alpha_d)\in\Bbb{Z}^d|\alpha_i\geqslant 1, \forall 1\leqslant i\leqslant d \text{and} \sum\limits_{i=1}^d\alpha_i=d+n-1\}$$ and \qa = (x_1^{\alpha_1},...,x_d^{\alpha_d}). Then we prove in this note that $M$ is a sequentially Cohen-Macaulay module if and only if there exists a certain system of parameters \x such that the equality \q^nM=\pd holds true for all $n$. As an application of this result, we can compute the Hilbert-Samuel polynomial of a sequentially Cohen-Macaulay module with respect to certain parameter idealsComment: 10 page

Analysis of MEMS electrostatic energy harvesters electrically configured as voltage multipliers

This paper presents the analysis of an efficient alternative interface circuit for MEMS electrostatic energy harvesters. It is entirely composed by diodes and capacitors. Based on modeling and simulation, the anti-phase gap-closing structure is investigated. We find that when configured as a voltage multiplier, it can operate at very low acceleration amplitudes. In addition, the allowed maximum voltage between electrodes is barely limited by the pull-in effect. The parasitic capacitance of the harvester and non-ideal characteristics of electronic components are taken into account. A lumped-model of the harvesting system has been implemented in a circuit simulator. Simulation results show that an output voltage of 22 V is obtained with 0.15 g input acceleration. The minimum necessary ratio between the maximum and minimum capacitances of the generators which allows operation of the circuit, can be lower than 2. This overcomes a crucial obstacle in low-power energy harvesting devices. A comparison between the voltage multiplier against other current topologies is highlighted. An advantage of the former over the latter is to generate much higher saturation voltage, while the minimum required initial bias and the minimum capacitance ratio in both cases are in the similar levels.Comment: 11 pages, IEEE journal article templat

On the lateral instability analysis of MEMS comb-drive electrostatic transducers

This paper investigates the lateral pull-in effect of an in-plane overlap-varying transducer. The instability is induced by the translational and rotational displacements. Based on the principle of virtual work, the equilibrium conditions of force and moment in lateral directions are derived. The analytical solutions of the critical voltage, at which the pull-in phenomenon occurs, are developed when considering only the translational stiffness or only the rotational stiffness of the mechanical spring. The critical voltage in general case is numerically determined by using nonlinear optimization techniques, taking into account the combined effect of translation and rotation. The effects of possible translational offsets and angular deviations to the critical voltage are modeled and numerically analyzed. The investigation is then the first time expanded to anti-phase operation mode and Bennet's doubler configuration of the two transducers.Comment: 16 page

Theoretical analysis of electrostatic energy harvester configured as Bennet's doubler based on Q-V cycles

This paper presents theoretical analysis of a MEMS electrostatic energy harvester configured as the Bennet's doubler. Steady-state operation of the doubler circuit can be approximated by a right-angled trapezoid Q-V cycle. A similarity between voltage doubler and resistive-based charge-pump circuit is highlighted. By taking electromechanical coupling into account, the analytical solution of the saturation voltage is the first time derived, providing a greater comprehension of the system performance and multi-parameter effects. The theoretical approach is verified by results of circuit simulation for two cases of mathematically idealized diode and of Schottky diode. Development of the doubler/multiplier circuits that can further increase the saturation voltage is investigated.Comment: 16 page