Finitistic dimension of monomial algebras

AbstractThe minimal projective resolution of the left ideal generated by any monomial p in a monomial algebra is described by a combinatorial object, the dimension tree of p. Two algorithms are proposed for computing the desired dimension trees. Determination of finitistic dimensions is then given as one of many homological applications which this idea might have

Research on Coordination Degree between Regional Marine Scientific and Technological Innovation and Blue Economic Development

There is a strong interactive coordination relationship between scientific and technological innovation and economic development and the coordinated development between the two has become a key factor in the healthy and sustainable development of regional economy This paper constructs the index system of regional marine scientific and technological innovation capability and blue economic development level and takes the data of blue economic zone of Shandong peninsula for 2005-2014 years as the sample to establish the coordination degree model The results show that the overall trend of coordination degree between marine scientific and technological innovation and blue economic development in Shandong blue economic zone is increasing year by year The coordination degree between regional marine scientific and technological innovation and blue economic development depends on the joint efforts of marine scientific and technological innovation and blue economic development and the lagging development of either side will hinder the promotion of coordination degre

COMPUTATIONAL STUDIES OF STRUCTURE–FUNCTION RELATIONSHIPS OF SUPPORTED AND UNSUPPORTED METAL NANOCLUSTERS

Fuel cells have been demonstrated to be promising power generation devices to address the current global energy and environmental challenges. One of the many barriers to commercialization is the cost of precious catalysts needed to achieve sufficient power output. Platinum-based materials play an important role as electrocatalysts in energy conversion technologies. In order to improve catalytic efficiency and facilitate rational design and development of new catalysts, structure–function relationships that underpin catalytic activity must be understood at a fundamental level. First, we present a systematic analysis of CO adsorption on Pt nanoclusters in the 0.2-1.5 nm size range with the aim of unraveling size-dependent trends and developing predictive models for site-specific adsorption behavior. Using an empirical-potential-based Genetic Algorithm (GA) and DFT modeling, we show that there exists a size window (40–70 atoms) over which Pt nanoclusters bind CO weakly, the binding energies being comparable to those on (111) or (100) facets. The size-dependent adsorption energy trends are, however, distinctly non-monotonic and are not readily captured using traditional descriptors such as d-band energies or (generalized) coordination numbers of the Pt binding sites. Instead, by applying machine-learning algorithms, we show that multiple descriptors, broadly categorized as structural and electronic descriptors, are essential for qualitatively capturing the CO adsorption trends. Nevertheless, attaining quantitative accuracy requires further refinement and we propose the use of an additional descriptor – the fully-frozen adsorption energy – that is a computationally inexpensive probe of CO–Pt bond formation. With these three categories of descriptors, we achieve an absolute mean error in CO adsorption energy prediction of 0.12 eV, which is similar to the underlying error of DFT adsorption calculations. Our approach allows for building quantitatively predictive models of site-specific adsorbate binding on realistic, low-symmetry nanostructures, which is an important step in modeling reaction networks as well as for rational catalyst design in general. Thereafter, to understand support effects on the activity of Pt nanoclusters, we employ a combination of empirical potential simulations and DFT calculations to investigate structure–function relationships of small PtN (N = 2-80) clusters on model carbon (graphene) supports. A bond-order empirical potential is employed within a GA to go beyond local optimizations in obtaining minimum-energy structures of PtN clusters on pristine as well as defective graphene supports. Point defects in graphene strongly anchor Pt clusters and also appreciably affect the morphologies of small clusters, which are characterized via various structural metrics such as the radius of gyration, average bond length, and average coordination number. A key finding from the structural analysis is that the fraction of potentially active surface sites in supported clusters is maximized for stable Pt clusters in the size range of 20-30 atoms, which provides a useful design criterion for optimal utilization of the precious metal. Through selected ab initio studies, we find a consistent trend for charge transfer from small Pt clusters to defective graphene supports resulting in the lowering of the cluster d-band center, which has implications for the overall activity and poisoning of the catalyst. The combination of a robust empirical potential-based GA for structural optimization with ab initio calculations opens up avenues for systematic studies of supported catalyst clusters at much larger system sizes than are accessible to purely ab initio approaches. Finally, we present a self-consistent charge density-functional tight-binding (SCC-DFTB) parameterization for PtRu alloys, which is developed by employing a training set of alloy cluster energies and forces obtained from Kohn-Sham DFT calculations. Extensive simulations of a testing set of PtRu alloy nanoclusters show that this SCC-DFTB scheme is capable of capturing cluster formation energies with high accuracy relative to DFT calculations. The new SCC-DFTB parameterization is employed within a GA to search for global minima of PtRu clusters in the range of 13-81 atoms and the emergence of Ru-core/Pt-shell structures at intermediate alloy compositions is systematically demonstrated. Our new SCC-DFTB parameterization enables computationally inexpensive modeling and exploration of structure–function relationships for Pt-Ru clusters that are among the best-performing catalysts in numerous energy applications

プロトコルの増強によるインターネットの機能向上

制度:新 ; 文部省報告番号:甲1961号 ; 学位の種類:博士(情報科学) ; 授与年月日:2004/10/28 ; 早大学位記番号:新386

CardioCam: Leveraging Camera on Mobile Devices to Verify Users While Their Heart is Pumping

With the increasing prevalence of mobile and IoT devices (e.g., smartphones, tablets, smart-home appliances), massive private and sensitive information are stored on these devices. To prevent unauthorized access on these devices, existing user verification solutions either rely on the complexity of user-defined secrets (e.g., password) or resort to specialized biometric sensors (e.g., fingerprint reader), but the users may still suffer from various attacks, such as password theft, shoulder surfing, smudge, and forged biometrics attacks. In this paper, we propose, CardioCam, a low-cost, general, hard-to-forge user verification system leveraging the unique cardiac biometrics extracted from the readily available built-in cameras in mobile and IoT devices. We demonstrate that the unique cardiac features can be extracted from the cardiac motion patterns in fingertips, by pressing on the built-in camera. To mitigate the impacts of various ambient lighting conditions and human movements under practical scenarios, CardioCam develops a gradient-based technique to optimize the camera configuration, and dynamically selects the most sensitive pixels in a camera frame to extract reliable cardiac motion patterns. Furthermore, the morphological characteristic analysis is deployed to derive user-specific cardiac features, and a feature transformation scheme grounded on Principle Component Analysis (PCA) is developed to enhance the robustness of cardiac biometrics for effective user verification. With the prototyped system, extensive experiments involving 25 subjects are conducted to demonstrate that CardioCam can achieve effective and reliable user verification with over 99% average true positive rate (TPR) while maintaining the false positive rate (FPR) as low as 4%

The neutrino-antineutrino annihilation to electron-positron pair around a Schwarzschild black hole in asymptotic safety

We research on the neutrino pair annihilation $\nu+\overline{\nu}\longrightarrow e^{-}+e^{+}$ around a massive source in asymptotic safety. The ratio $\frac{\dot{Q}}{\dot{Q}_{Newt}}$ corresponding to the energy deposition per unit time over that in the Newtonian case is derived and calculated. We find that the quantum corrections to the black hole spacetime affect the emitted energy rate ratio for the annihilation. It is interesting that the more considerable quantum effect reduces the ratio value slightly. The corrected annihilation process can become a source of gamma ray burst. We also investigate the derivative $\frac{d\dot{Q}}{dr}$ relating to the star's radius $r$ to show that the quantum effect for the black hole will drop the ratio. The more manifest quantum gravity influence leads the weaker neutrino pair annihilation.Comment: 10 pages, 2 figures. arXiv admin note: text overlap with arXiv:2206.0067

Power Scaling of Uplink Massive MIMO Systems with Arbitrary-Rank Channel Means

This paper investigates the uplink achievable rates of massive multiple-input multiple-output (MIMO) antenna systems in Ricean fading channels, using maximal-ratio combining (MRC) and zero-forcing (ZF) receivers, assuming perfect and imperfect channel state information (CSI). In contrast to previous relevant works, the fast fading MIMO channel matrix is assumed to have an arbitrary-rank deterministic component as well as a Rayleigh-distributed random component. We derive tractable expressions for the achievable uplink rate in the large-antenna limit, along with approximating results that hold for any finite number of antennas. Based on these analytical results, we obtain the scaling law that the users' transmit power should satisfy, while maintaining a desirable quality of service. In particular, it is found that regardless of the Ricean $K$-factor, in the case of perfect CSI, the approximations converge to the same constant value as the exact results, as the number of base station antennas, $M$, grows large, while the transmit power of each user can be scaled down proportionally to $1/M$. If CSI is estimated with uncertainty, the same result holds true but only when the Ricean $K$-factor is non-zero. Otherwise, if the channel experiences Rayleigh fading, we can only cut the transmit power of each user proportionally to $1/\sqrt M$. In addition, we show that with an increasing Ricean $K$-factor, the uplink rates will converge to fixed values for both MRC and ZF receivers