Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals

We present criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen-Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen-Macaulayness of the second symbolic power or of all symbolic powers of a Stanley-Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen-Macaulay. In particular, all symbolic powers are Cohen-Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen-Macaulayness can pass from a symbolic power to another symbolic powers in different ways.Comment: The published version of this paper contains a gap in the proofs of Theorem 2.5 and Theorem 3.5. This version corrects the proofs with almost the same arguments. Moreover, we have to modify the definition of tight complexes in Theorem 2.5. These changes don't affect other things in the published version. A corrigendum has been sent to the journa

EVOLUTION OF THE HOTEL BUSINESS SECTOR AND SUSTAINABLE TOURISM DEVELOPMENT IN HOTEL BUSINESS: A STUDY IN VIETNAM

In tandem with the global expansion of the hotel industry, the hotel business market in Vietnam is also experiencing significant growth, occupying a pivotal position in the country's economy. According to UNWTO, Vietnam is ranked 6th out of 10 countries with the highest tourist growth rate worldwide, and it has been selected as a leading tourist destination in Asia by WTA. However, this rapid growth comes with adverse effects on resource, environmental, and cultural concerns. These manifestations signify unsustainable development. Consequently, the need for sustainable tourism development, specifically green tourism, has become an imperative requirement. This demands concerted efforts from the Vietnamese tourism industry as a whole and tourism enterprises, including hotels, to achieve this goal. This article delves into the realm of green tourism development and its application within the hotel business sector in Vietnam

Improved Time and Frequency Synchronization Algorithm for 802.11a Wireless Standard based on the SIGNAL Field

International audienceTime and frequency synchronization in the IEEE 802.11a OFDM (Orthogonal Frequency Division Multiplexing) wireless communication system is addressed in this paper. Usually synchronization algorithms rely only on training sequences specified by the standard. To enhance the synchronization between stations, we propose to extract known information by both the transmitter and the receiver at the IEEE 802.11a physical layer to be then exploited by the receiver in addition to the training sequences. Indeed the parts of the identified SIGNAL field are either known or predictable from the RtS (Request to Send) control frame when the CSMA/CA (Carrier Sense Multiple Access with Collision Avoidance) mechanism is triggered jointly to bit-rate adaptation algorithms to the channel. Moreover the received RtS control frame allows the receiver to estimate the channel before time synchronization stage improving then the performance of the proposed synchronization algorithm. Simulation results show that the performance of the proposed synchronization algorithm is improved as compared to existing algorithms

Depth of powers of edge ideals of cycles and trees

Let $I$ be the edge ideal of a cycle of length $n \ge 5$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_n]$. We prove that for $2 \le t < \lceil (n+1)/2 \rceil$, $$\operatorname{depth} (S/I^t) = \lceil \frac{n -t + 1}{3} \rceil.$$ When $G = T_{\mathbf{a}}$ is a starlike tree which is the join of $k$ paths of length $a_1, \ldots, a_k$ at a common root $1$, we give a formula for the depth of powers of $I(T_{\mathbf{a}})$

Factors of Purchase Intentions toward Foreign Products: Empirical Evidence from Vietnamese Consumers’ Perspective

This study empirically explores factors affecting consumers’ purchase intentions toward foreign products, and their impact magnitudes in six major cities of Vietnam (including Ha Noi, Hai Phong, Da Nang, Ho Chi Minh, Binh Duong, and Can Tho). Our results illustrate that Vietnamese consumers’ purchase intentions toward foreign products are positively affected by Perceived quality, Perceived prestige, Perceived value, and Influence of others. Notably, Perceived prestige has the strongest impact on consumers’ purchase intentions. The findings of this study enrich the international marketing literature on the consumer evaluation of foreign products in developing countries like Vietnam as well as assist practitioners to build more appropriate marketing strategies for targeting emerging markets

Seawater desalination using air gap membrane distillation-an experimental study on membrane scaling and cleaning

The connection between operating temperature and membrane scaling/cleaning during an air gap membrane distillation (AGMD) process of seawater has been systematically elucidated in this study. Experimental and mathematically simulated data demonstrate the profound influences of feed salinity and membrane scaling on water flux at various operating temperatures. Feed salinity exerted significant impacts on water flux at high operating temperatures because of aggravated polarization effects. Membrane scaling and the subsequent membrane cleaning efficiency were also strongly affected by operating temperatures. Indeed, membrane scaling was more severe and occurred at a lower water recovery when operating at 60-50 °C (feed-coolant temperature) compared to that at 35-25 °C. Moreover, membrane cleaning with fresh water and vinegar was less effective for the membrane scaled at 60-50 °C compared to 35-25 °C. Finally, membrane cleaning using vinegar was much more efficient than fresh water. Given the availability of vinegar at household level, vinegar cleaning can potentially be a low cost and readily accessible approach for MD maintenance for small scale seawater desalination applications in remote coastal communities