The determinantal ideals of extended Hankel matrices

In this paper, we use the tools of Gr\"{o}bner bases and combinatorial secant varieties to study the determinantal ideals $I_t$ of the extended Hankel matrices. Denote by $c$-chain a sequence $a_1,\...,a_k$ with $a_i+c<a_{i+1}$ for all $i=1,\...,k-1$. Using the results of $c$-chain, we solve the membership problem for the symbolic powers $I_t^{(s)}$ and we compute the primary decomposition of the product $I_{t_1}\... I_{t_k}$ of the determinantal ideals. Passing through the initial ideals and algebras we prove that the product $I_{t_1}\... I_{t_k}$ has a linear resolution and the multi-homogeneous Rees algebra \Rees(I_{t_1},\...,I_{t_k}) is defined by a Gr\"obner basis of quadrics

The standard graded property for vertex cover algebras of Quasi-Trees

J. Herzog, T. Hibi, N. V. Trung and X. Zheng characterize the vertex cover algebras which are standard graded. In this paper we give a simple combinatorial criterion for the standard graded property of vertex cover algebras in the case of quasi-trees. We also give an example of how this criterion works and compute the maximal degree of a minimal generator in that case

Cohen-Macaulayness of generically complete intersection monomial ideals

In this paper we discuss the problem of characterizing the Cohen-Macaulay property of certain families of monomial ideals with fixed radical. More precisely, we consider generically complete intersection monomial ideals whose radical corresponds to special classes of simplicial complexes.Comment: To appear in Comm. Al

A Knowledge-Based Model For Context-Aware Smart Service Systems

The advancement of the Internet of Things, big data, and mobile computing leads to the need for smart services that enable the context awareness and the adaptability to their changing contexts. Today, designing a smart service system is a complex task due to the lack of an adequate model support in awareness and pervasive environment. In this paper, we present the concept of a context-aware smart service system and propose a knowledge model for context-aware smart service systems. The proposed model organizes the domain and context-aware knowledge into knowledge components based on the three levels of services: Services, Service system, and Network of service systems. The knowledge model for context-aware smart service systems integrates all the information and knowledge related to smart services, knowledge components, and context awareness that can play a key role for any framework, infrastructure, or applications deploying smart services. In order to demonstrate the approach, two case studies about chatbot as context-aware smart services for customer support are presented

An Efficient Precoder Design for Multiuser MIMO Cognitive Radio Networks with Interference Constraints

We consider a linear precoder design for an underlay cognitive radio multiple-input multiple-output broadcast channel, where the secondary system consisting of a secondary base-station (BS) and a group of secondary users (SUs) is allowed to share the same spectrum with the primary system. All the transceivers are equipped with multiple antennas, each of which has its own maximum power constraint. Assuming zero-forcing method to eliminate the multiuser interference, we study the sum rate maximization problem for the secondary system subject to both per-antenna power constraints at the secondary BS and the interference power constraints at the primary users. The problem of interest differs from the ones studied previously that often assumed a sum power constraint and/or single antenna employed at either both the primary and secondary receivers or the primary receivers. To develop an efficient numerical algorithm, we first invoke the rank relaxation method to transform the considered problem into a convex-concave problem based on a downlink-uplink result. We then propose a barrier interior-point method to solve the resulting saddle point problem. In particular, in each iteration of the proposed method we find the Newton step by solving a system of discrete-time Sylvester equations, which help reduce the complexity significantly, compared to the conventional method. Simulation results are provided to demonstrate fast convergence and effectiveness of the proposed algorithm.Comment: Accepted to appear in IEEE Trans. Vehicular Technology, 13 pages, 8 figure

When does depth stabilize early on?

In this paper we study graded ideals I in a polynomial ring S such that the numerical function f(k)=depth(S/I^k) is constant. We show that, if (i) the Rees algebra of I is Cohen-Macaulay, (ii) the cohomological dimension of I is not larger than the projective dimension of S/I and (iii) the K-algebra generated by some generators of I is a direct summand of S, then f(k) is constant. When I is a square-free monomial ideal, the above criterion includes as special cases all the results of a recent paper by Herzog and Vladoiu. In this combinatorial setting there is a chance that the converse of the above fact holds true.Comment: The title has been changed and other minor changes have been done. The paper will appear in Journal of Algebr

Gravity terrain correction for mainland territory of Vietnam

Terrain corrections for gravity data are a critical concern in rugged topography, because the magnitude of the corrections may be largely relative to the anomalies of interest. That is also important to determine the inner and outer radii beyond which the terrain effect can be neglected. Classical methods such as Lucaptrenco, Beriozkin and Prisivanco are indeed too slow with radius correction and are not extended while methods based on the Nagy’s and Kane’s are usually too approximate for the required accuracy. In order to achieve 0.1 mGal accuracy in terrain correction for mainland territory of Vietnam and reduce the computing time, the best inner and outer radii for terrain correction computation are 2 km and 70 km respectively. The results show that in nearly a half of the Vietnam territory, the terrain correction values ≥ 10 mGal, the corrections are smaller in the plain areas (less than 2 mGal) and higher in the mountainous region, in particular the correction reaches approximately 21 mGal in some locations of northern mountainous region. The complete Bouguer gravity map of mainland territory of Vietnam is reproduced based on the full terrain correction introduced in this paper

Study on structure of the Earth’s crust in Thua Thien-Hue province and adjacent areas by using gravity and magnetic data in combination

This paper presents the structural characteristics of the Earth’s crust in Thua Thien-Hue province and adjacent area based on interpretation of gravity and magnetic data in combination. Research results have shown that: The depth of crystalline basement varies complicatedly, in the range of 0–11 km. The depth of Conrad surface increases from Northeast (12 km) to Southwest (18 km) and the depth of Moho surface is 23–34 km; The density of sedimentary layer changes from 2.61 g/cm3 to 2.65 g/cm3. Meanwhile, the density of granitic layer is in the range of 2.68–2.73 g/cm3. The basaltic layer has the density value of 2.88–2.93 g/cm3 and the average density of lower layer of the Earth’s crust is about 3.30 g/cm3; The depth of second-order faults, Red River and A Luoi - Rao Quan, is through the Earth’s crust. Meanwhile, the depth of influence of third-order faults, Chay river, Dong Ha - Phu Vang, Vinh Linh, Hue - Son Tra and Tam Ky - Phuoc Son, is within the thickness of the Earth’s crust

Preparation and characterization of magnesium hydroxyapatite coatings on 316L stainless steel

Magnesium hydroxyapatite coatings (MgHAp) were deposited on the surface of 316L stainless steel (316L SS) substrates by electrodeposition technique. Different concentrations of Mg2+ ion were incorporated into the apatite structure by adding Mg(NO3)2 into electrolyte solution containing 3×10-2 M Ca(NO3)2, 1.8×10-2 M NH4H2PO4 and   6×10-2 M NaNO3. With Mg2+ concentration 1×10-3 M, the obtained coatings have 0.2 wt% Mg2+. The influences of scanning potential ranges, scanning times to deposit MgHAp coatings were researched. The analytical results FTIR, SEM, X-ray, EDX, thickness and adhension strength showed that MgHAp coatings were single phase of HAp, fibrous shapes, thickness 8.1 µm and adhesion strength 7.20 MPa at the scanning potential ranges of 0÷-1.7 V/SCE and scanning times of 5 scans. Keywords. 316L SS, Electrodeposition, MgHAp