The reconstruction of an hermitian Toeplitz matrices with prescribed eigenpairs

In this paper we concern the reconstruction of an hermitian Toeplitz matrices with prescribed eigenpairs. Based on the fact that every centrohermitian matrix can be re- duced to a real matrix by a simple similarity transformation, we rst consider the eigenstructure of hermitian Toeplitz matrices and then discuss a related reconstruction problem. We show that the di- mension of the subspace of hermitian Toeplitz matrices with two given eigenvectors is at least two and independent of the size of the matrix, and the solution of the reconstruction problem of an hermitian Toeplitz matrix with two given eigenpairs is unique.Fundação para a Ciência e a Tecnologia (FCT) - Research Programme POCTINational Natural Science Foundation of China - nº 10771022, 10571012Scienti c Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry of China - nº 890 (2008)Major Foundation of Educational Committee of Hunan Province - nº 09A002 (2009

Impact of Default Distance on Financial Warning of Listed Companies

Distance to Default is a measure of credit risk based on stock trading data. According to the result, the default distance can improve the goodness of fit and forecasting ability of the financial early-warning model, but the improvement effect is limited. And with the increasingly fierce market competition, the impact of financial risk on the survival and development of enterprises is also growing. Modern enterprises must fully understand the causes of financial risks, establish and improve risk control mechanisms, prevent and resolve various financial risks in the development of enterprises, To ensure that the development of enterprises toward a reasonable, scientific and healthy direction. Keywords: default distance, financial crisis, financial warnin

7-Bromo-4-(7-bromo-3,3-dimethyl-1-oxo-2,3,4,9-tetra­hydro-1H-xanthen-9-yl)-3,3-dimethyl-2,3-dihydroxanthen-1(4H)-one ethanol solvate

The title compound, C30H26Br2O4·C2H5OH, was synthesized from the reaction between 5-bromo­salicybenzaldehyde and 5,5-dimethyl-1,3-cyclo­hexa­nedione. The crystal packing is stabilized by inter­molecular O—H⋯O hydrogen bonds and C—H⋯O inter­actions

14-Methoxy-2,16-dioxapentacyclo[7.7.5.01,21.03,8.010,15]henicosa-3(8),10,12,14-tetraene-7,20-dione

The title compound, C20H20O5, was synthesized from the reaction between 3-methoxysalicaldehyde and 1,3–cyclo­hexa­nedione in the presence of palladium(II) chloride. The two fused xanthene rings and one of the six-membered cyclo­hexane rings adopt envelope conformations, while the other six-membered cyclo­hexane ring is in a chair conformation. The mol­ecular packing is stabilized by weak inter­molecular C—H⋯O inter­actions

Channel Cycle Time: A New Measure of Short-term Fairness

This paper puts forth a new metric, dubbed channel cycle time (CCT), to measure the short-term fairness of communication networks. CCT characterizes the average duration between two consecutive successful transmissions of a user, during which all other users successfully accessed the channel at least once. In contrast to existing short-term fairness measures, CCT provides more comprehensive insight into the transient dynamics of communication networks, with a particular focus on users' delays and jitter. To validate the efficacy of our approach, we analytically characterize the CCTs for two classical communication protocols: slotted Aloha and CSMA/CA. The analysis demonstrates that CSMA/CA exhibits superior short-term fairness over slotted Aloha. Beyond its role as a measurement metric, CCT has broader implications as a guiding principle for the design of future communication networks by emphasizing factors like fairness, delay, and jitter in short-term behaviors

9-(4-Chloro­phen­yl)-4a-hy­droxy-4,4a,5,6,9,9a-hexa­hydro-3H-xanthene-1,8(2H,7H)-dione

In the title compound, C19H19ClO4, the central fused ring and the attached cyclo­hexene ring adopt envelope conformations, while the cyclo­hexane ring adopts a chair conformation. The crystal packing is stabilized by O—H⋯O hydrogen bonds, which link the mol­ecules into a chain along the b axis. Weak C—H⋯O bonds also occur

Stability of Y/MCM-48 composite molecular sieve with mesoporous and microporous structures

AbstractY/MCM-48 composite molecular sieve was hydrothermally synthesized at different crystallization temperatures and crystallization times using ethyl orthosilicate as Si source and cetyltrimethyl ammonium bromide as template with the aid of fluoride ions and was characterized by X-ray diffraction, N2 physical adsorption technique, scanning electron microscopy and transmission electron microscopy. The thermal, hydrothermal, acidic, and basic stabilities of the Y/MCM-48 composite were investigated. The results show that Y/MCM-48 composite molecular sieve with meso- and microporous structures was synthesized successfully at 120°C for 36h. The Y/MCM-48 composite has the surface area of 864m2/g and the average pore size is ca. 2.48nm. The bi-porous structure in composite molecular sieve still maintains its stability even after thermal treatment at 800°C for 4h or hydrothermal treatment at 100°C for 48h. After treatment in 1mol/L hydrochloric acid solution or 1mol/L sodium hydroxide solution for 48h, the Y/MCM-48 composite exhibits good acidic stability. The acidic stability is superior to the basic stability at the same treatment time